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`

tsconfig.json

@@ -0,0 +1,30 @@
+{
+  "include": [
+    "*",
+    "tests/e2e/**/*",
+    "tools/**/*",
+    "web_src/js/**/*",
+  ],
+  "compilerOptions": {
+    "target": "es2020",
+    "module": "node16",
+    "moduleResolution": "node16",
+    "lib": ["dom", "dom.iterable", "dom.asynciterable", "esnext"],
+    "allowImportingTsExtensions": true,
+    "allowJs": true,
+    "allowSyntheticDefaultImports": true,
+    "alwaysStrict": true,
+    "esModuleInterop": true,
+    "isolatedModules": true,
+    "noEmit": true,
+    "resolveJsonModule": true,
+    "skipLibCheck": true,
+    "verbatimModuleSyntax": true,
+    "stripInternal": true,
+    "strict": false,
+    "noUnusedLocals": true,
+    "noUnusedParameters": true,
+    "noPropertyAccessFromIndexSignature": false,
+    "exactOptionalPropertyTypes": false,
+  }
+}