Add type checking workflow

Based on https://github.com/voxpelli/ghatemplates/blob/main/.github/workflows/type-check.yml which I use in eg. https://github.com/voxpelli/pony-cause/blob/main/.github/workflows/ts.yml and https://github.com/voxpelli/pony-cause/blob/main/.github/workflows/ts-internal.yml

Author: voxpelli

.eslintignore

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+test-published-types

.github/workflows/type-check.yml

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+name: "Types: check published types"
+
+on: [pull_request, push]
+
+permissions:
+  contents: read
+
+jobs:
+  test:
+    name: TS ${{ matrix.ts_version }}, "${{ matrix.ts_lib }}"
+    runs-on: ubuntu-latest
+    strategy:
+      fail-fast: false
+      matrix:
+        ts_version:
+          # The official ESLint types are not compatible with TS 3.9
+          # - 3.9
+          - '4.0'
+          - 4.1
+          - 4.2
+          - 4.3
+          - 4.4
+          - 4.5
+          - '5.0'
+          - 5.5
+          - 5.6
+        ts_lib:
+          - es2015
+          - es2015,dom
+          - es2020
+          - esnext
+    steps:
+      - uses: actions/checkout@v4
+        with:
+          persist-credentials: false
+          show-progress: false
+
+      - uses: ljharb/actions/node/install@main
+        name: 'nvm install lts/* && npm install'
+        with:
+          node-version: 'lts/*'
+          skip-ls-check: true
+
+      - name: build types
+        run: npm run build-types
+
+      - name: npm install working directory
+        run: npm install --ignore-scripts
+        working-directory: test-published-types
+
+      - name: install typescript version ${{ matrix.ts_version }}
+        run: npm install --force typescript@${{ matrix.ts_version }}
+        working-directory: test-published-types
+
+      - name: show installed typescript version
+        run: npm list typescript --depth=0
+        working-directory: test-published-types
+
+      - name: check types with lib "${{ matrix.ts_lib }}"
+        run: npx tsc --lib ${{ matrix.ts_lib }}
+        working-directory: test-published-types

test-published-types/.npmrc

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+package-lock=false

test-published-types/index.js

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+'use strict';
+
+const react = require('eslint-plugin-react');
+
+/** @type {import('eslint').Linter.Config[]} */
+module.exports = [
+  {
+    plugins: {
+      react,
+    },
+  },
+];

test-published-types/package.json

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+{
+  "name": "eslint-plugin-react-test-published-types",
+  "private": true,
+  "version": "0.0.0",
+  "dependencies": {
+    "@eslint/core": "^0.6.0",
+    "@types/estree": "^1.0.6",
+    "@types/json-schema": "^7.0.15",
+    "eslint": "^9.0.0",
+    "eslint-plugin-react": "file:.."
+  }
+}

test-published-types/tsconfig.json

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+{
+  "extends": "../tsconfig.json",
+
+  "files": [
+    "index.js"
+  ],
+
+  "compilerOptions": {
+    "lib": ["esnext"],
+    "types": ["node"]
+  }
+}