Add initial typescript config and use it for eslint,vitest,playwright (#31186)

This enables eslint to use the typescript parser and resolver which
brings some benefits that eslint rules now have type information
available and a tsconfig.json is required for the upcoming typescript
migration as well. Notable changes done:

- Add typescript parser and resolver
- Move the vue-specific config into the root file
- Enable `vue-scoped-css/enforce-style-type` rule, there was only one
violation and I added a inline disable there.
- Fix new lint errors that were detected because of the parser change
- Update `i/no-unresolved` to remove now-unnecessary workaround for the
resolver
- Disable `i/no-named-as-default` as it seems to raise bogus issues in
the webpack config
- Change vitest config to typescript
- Change playwright config to typescript
- Add `eslint-plugin-playwright` and fix issues
- Add `tsc` linting to `make lint-js`

vitest.config.ts

@@ -0,0 +1,21 @@
+import {defineConfig} from 'vitest/config';
+import vuePlugin from '@vitejs/plugin-vue';
+import {stringPlugin} from 'vite-string-plugin';
+
+export default defineConfig({
+  test: {
+    include: ['web_src/**/*.test.js'],
+    setupFiles: ['web_src/js/vitest.setup.js'],
+    environment: 'happy-dom',
+    testTimeout: 20000,
+    open: false,
+    allowOnly: true,
+    passWithNoTests: true,
+    globals: true,
+    watch: false,
+  },
+  plugins: [
+    stringPlugin(),
+    vuePlugin(),
+  ],
+});