React Native -> React Native Web with webpack and JSX

I started a new React Native project (v61.5) with the TypeScript template (npx react-native init MyTSProject --template react-native-template-typescript). It compiles fine with React Native but when I try to add webpack (for React Native Web) I get JSX/TSX errors (I think). Am I doing something wrong with webpack here?

tsconfig.json

{
  "compilerOptions": {
    /* Basic Options */
    "target": "es5",                          /* Specify ECMAScript target version: 'ES3' (default), 'ES5', 'ES2015', 'ES2016', 'ES2017','ES2018' or 'ESNEXT'. */
    "module": "commonjs",                     /* Specify module code generation: 'none', 'commonjs', 'amd', 'system', 'umd', 'es2015', or 'ESNext'. */
    "lib": [ "es5", "es6", "dom" ],           /* Specify library files to be included in the compilation. */
    "allowJs": true,                          /* Allow javascript files to be compiled. */
    // "checkJs": true,                       /* Report errors in .js files. */
    "jsx": "react-native",                    /* Specify JSX code generation: 'preserve', 'react-native', or 'react'. */
    // "declaration": true,                   /* Generates corresponding '.d.ts' file. */
    // "sourceMap": true,                     /* Generates corresponding '.map' file. */
    // "outFile": "./",                       /* Concatenate and emit output to single file. */
    // "outDir": "./",                        /* Redirect output structure to the directory. */
    // "rootDir": "./",                       /* Specify the root directory of input files. Use to control the output directory structure with --outDir. */
    "removeComments": true,                   /* Do not emit comments to output. */
    // "noEmit": true,                        /* Do not emit outputs. */
    "incremental": true,                      /* Enable incremental compilation */
    "importHelpers": true,                    /* Import emit helpers from 'tslib'. */
    "downlevelIteration": true,               /* Provide full support for iterables in 'for-of', spread, and destructuring when targeting 'ES5' or 'ES3'. */
    "isolatedModules": true,                  /* Transpile each file as a separate module (similar to 'ts.transpileModule'). */

    /* Strict Type-Checking Options */
    "strict": true,                           /* Enable all strict type-checking options. */
    // "noImplicitAny": true,                 /* Raise error on expressions and declarations with an implied 'any' type. */
    // "strictNullChecks": true,              /* Enable strict null checks. */
    // "strictFunctionTypes": true,           /* Enable strict checking of function types. */
    // "strictPropertyInitialization": true,  /* Enable strict checking of property initialization in classes. */
    // "noImplicitThis": true,                /* Raise error on 'this' expressions with an implied 'any' type. */
    // "alwaysStrict": true,                  /* Parse in strict mode and emit "use strict" for each source file. */

    /* Additional Checks */
    // "noUnusedLocals": true,                /* Report errors on unused locals. */
    // "noUnusedParameters": true,            /* Report errors on unused parameters. */
    // "noImplicitReturns": true,             /* Report error when not all code paths in function return a value. */
    // "noFallthroughCasesInSwitch": true,    /* Report errors for fallthrough cases in switch statement. */

    /* Module Resolution Options */
    "moduleResolution": "node",               /* Specify module resolution strategy: 'node' (Node.js) or 'classic' (TypeScript pre-1.6). */
    "baseUrl": "./",                          /* Base directory to resolve non-absolute module names. */
    // "paths": {},                           /* A series of entries which re-map imports to lookup locations relative to the 'baseUrl'. */
    // "rootDirs": [],                        /* List of root folders whose combined content represents the structure of the project at runtime. */
    // "typeRoots": [],                       /* List of folders to include type definitions from. */
    // "types": [],                           /* Type declaration files to be included in compilation. */
    "allowSyntheticDefaultImports": true,     /* Allow default imports from modules with no default export. This does not affect code emit, just typechecking. */
    "esModuleInterop": true,                  /* Enables emit interoperability between CommonJS and ES Modules via creation of namespace objects for all imports. Implies 'allowSyntheticDefaultImports'. */
    // "preserveSymlinks": true,              /* Do not resolve the real path of symlinks. */

    /* Source Map Options */
    // "sourceRoot": "./",                    /* Specify the location where debugger should locate TypeScript files instead of source locations. */
    // "mapRoot": "./",                       /* Specify the location where debugger should locate map files instead of generated locations. */
    // "inlineSourceMap": true,               /* Emit a single file with source maps instead of having a separate file. */
    // "inlineSources": true,                 /* Emit the source alongside the sourcemaps within a single file; requires '--inlineSourceMap' or '--sourceMap' to be set. */

    /* Experimental Options */
    // "experimentalDecorators": true,        /* Enables experimental support for ES7 decorators. */
    // "emitDecoratorMetadata": true,         /* Enables experimental support for emitting type metadata for decorators. */

    "resolveJsonModule": true,
  },
  "exclude": [
    "node_modules", "babel.config.js", "metro.config.js", "jest.config.js"
  ]
}

webpack.config.js

const path = require('path');
const webpack = require('webpack');
const HtmlWebpackPlugin = require('html-webpack-plugin');
const rootDir = path.join(__dirname, '..');
const webpackEnv = process.env.NODE_ENV || 'development';

module.exports = {
  mode: webpackEnv,
  entry: {
    app: path.join(rootDir, './index.web.ts'),
  },
  output: {
    path: path.resolve(rootDir, 'dist'),
    filename: 'app-[hash].bundle.js',
  },
  devtool: 'source-map',
  module: {
    rules: [
      {
        test: /\.(tsx|ts|jsx|js|mjs)$/,
        exclude: /node_modules/,
        use: [ 'ts-loader' ],
      },
    ],
  },
  plugins: [
    new HtmlWebpackPlugin({
      template: path.join(__dirname, './index.html'),
    }),
    new webpack.HotModuleReplacementPlugin(),
  ],
  resolve: {
    extensions: [
      '.web.tsx',
      '.web.ts',
      '.tsx',
      '.ts',
      '.web.jsx',
      '.web.js',
      '.jsx',
      '.js',
    ], // read files in following order
    alias: Object.assign({
      'react-native$': 'react-native-web',
    }),
  },
};

TypeScript (As from the React Native demo app) import React from 'react'; import { SafeAreaView, StyleSheet, ScrollView, View, Text, StatusBar, } from 'react-native';

import {
  Header,
  LearnMoreLinks,
  Colors,
  DebugInstructions,
  ReloadInstructions,
} from 'react-native/Libraries/NewAppScreen';

declare var global: {HermesInternal: null | {}};

const App = () => {
  return (
    <>
      <StatusBar barStyle="dark-content" />
      <SafeAreaView>
        <ScrollView
          contentInsetAdjustmentBehavior="automatic"
          style={styles.scrollView}>
          <Header />
          {global.HermesInternal == null ? null : (
            <View style={styles.engine}>
              <Text style={styles.footer}>Engine: Hermes</Text>
            </View>
          )}
          <View style={styles.body}>
            <View style={styles.sectionContainer}>
              <Text style={styles.sectionTitle}>Step One</Text>
              <Text style={styles.sectionDescription}>
                Edit <Text style={styles.highlight}>App.tsx</Text> to change this
                screen and then come back to see your edits.
              </Text>
            </View>
            <View style={styles.sectionContainer}>
              <Text style={styles.sectionTitle}>See Your Changes</Text>
              <Text style={styles.sectionDescription}>
                <ReloadInstructions />
              </Text>
            </View>
            <View style={styles.sectionContainer}>
              <Text style={styles.sectionTitle}>Debug</Text>
              <Text style={styles.sectionDescription}>
                <DebugInstructions />
              </Text>
            </View>
            <View style={styles.sectionContainer}>
              <Text style={styles.sectionTitle}>Learn More</Text>
              <Text style={styles.sectionDescription}>
                Read the docs to discover what to do next:
              </Text>
            </View>
            <LearnMoreLinks />
          </View>
        </ScrollView>
      </SafeAreaView>
    </>
  );
};

const styles = StyleSheet.create({
  scrollView: {
    backgroundColor: Colors.lighter,
  },
  engine: {
    position: 'absolute',
    right: 0,
  },
  body: {
    backgroundColor: Colors.white,
  },
  sectionContainer: {
    marginTop: 32,
    paddingHorizontal: 24,
  },
  sectionTitle: {
    fontSize: 24,
    fontWeight: '600',
    color: Colors.black,
  },
  sectionDescription: {
    marginTop: 8,
    fontSize: 18,
    fontWeight: '400',
    color: Colors.dark,
  },
  highlight: {
    fontWeight: '700',
  },
  footer: {
    color: Colors.dark,
    fontSize: 12,
    fontWeight: '600',
    padding: 4,
    paddingRight: 12,
    textAlign: 'right',
  },
});

export default App;

Output/Error

ℹ ｢wds｣: Project is running at http://localhost:8080/
ℹ ｢wds｣: webpack output is served from /
ℹ ｢wds｣: Content not from webpack is served from /home/nick/MyTSProject/web
✖ ｢wdm｣: Hash: e739fe310ea105fb05fe
Version: webpack 4.41.5
Time: 4672ms
Built at: 12/30/2019 8:13:55 PM
                                 Asset       Size  Chunks                         Chunk Names
    app-e739fe310ea105fb05fe.bundle.js   2.48 MiB     app  [emitted] [immutable]  app
app-e739fe310ea105fb05fe.bundle.js.map   2.63 MiB     app  [emitted] [dev]        app
                            index.html  438 bytes          [emitted]              
Entrypoint app = app-e739fe310ea105fb05fe.bundle.js app-e739fe310ea105fb05fe.bundle.js.map
[0] multi ../node_modules/webpack-dev-server/client?http://localhost:8080 ../index.web.ts 40 bytes {app} [built]
[../app.json] 60 bytes {app} [built]
[../index.web.ts] 496 bytes {app} [built]
[../node_modules/react-native-web/dist/index.js] 4.3 KiB {app} [built]
[../node_modules/tslib/tslib.es6.js] 9.21 KiB {app} [built]
[../node_modules/webpack-dev-server/client/index.js?http://localhost:8080] ../node_modules/webpack-dev-server/client?http://localhost:8080 4.29 KiB {app} [built]
[../node_modules/webpack-dev-server/client/overlay.js] 3.51 KiB {app} [built]
[../node_modules/webpack-dev-server/client/socket.js] 1.53 KiB {app} [built]
[../node_modules/webpack-dev-server/client/utils/createSocketUrl.js] 2.91 KiB {app} [built]
[../node_modules/webpack-dev-server/client/utils/log.js] 964 bytes {app} [built]
[../node_modules/webpack-dev-server/client/utils/reloadApp.js] 1.59 KiB {app} [built]
[../node_modules/webpack-dev-server/client/utils/sendMessage.js] 402 bytes {app} [built]
[../node_modules/webpack-dev-server/node_modules/strip-ansi/index.js] 161 bytes {app} [built]
[../node_modules/webpack/hot sync ^\.\/log$] ../node_modules/webpack/hot sync nonrecursive ^\.\/log$ 170 bytes {app} [built]
[../source/App.tsx] 438 bytes {app} [built] [failed] [1 error]
    + 255 hidden modules

ERROR in ../source/App.tsx 8:12
Module parse failed: Unexpected token (8:12)
File was processed with these loaders:
 * ../node_modules/ts-loader/index.js
You may need an additional loader to handle the result of these loaders.
| var NewAppScreen_1 = require("react-native/Libraries/NewAppScreen");
| var App = function () {
>     return (<>
|       <react_native_1.StatusBar barStyle="dark-content"/>
|       <react_native_1.SafeAreaView>
 @ ../index.web.ts 6:36-59
Child html-webpack-plugin for "index.html":
     1 asset
    Entrypoint undefined = index.html
    [../node_modules/html-webpack-plugin/lib/loader.js!./index.html] 566 bytes {0} [built]
    [../node_modules/lodash/lodash.js] 528 KiB {0} [built]
    [../node_modules/webpack/buildin/global.js] 472 bytes {0} [built]
    [../node_modules/webpack/buildin/module.js] 497 bytes {0} [built]
ℹ ｢wdm｣: Failed to compile.

I have tried alternative loaders (babel-loader, awesome-typescript-loader). I have tried various chat rooms. I have read many, many blog posts (although they almost all seem to be from years ago and no longer apply).

No idea where to go from here.