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`

Makefile

@@ -375,11 +375,13 @@ lint-backend-fix: lint-go-fix lint-go-vet lint-editorconfig
 
 .PHONY: lint-js
 lint-js: node_modules
-	npx eslint --color --max-warnings=0 --ext js,vue $(ESLINT_FILES)
+	npx eslint --color --max-warnings=0 --ext js,ts,vue $(ESLINT_FILES)
+	npx tsc
 
 .PHONY: lint-js-fix
 lint-js-fix: node_modules
-	npx eslint --color --max-warnings=0 --ext js,vue $(ESLINT_FILES) --fix
+	npx eslint --color --max-warnings=0 --ext js,ts,vue $(ESLINT_FILES) --fix
+	npx tsc
 
 .PHONY: lint-css
 lint-css: node_modules