Update lit-starter-ts to lit-next

* Upgrades the source to work with lit-next
* Aligns the linting and formatting rules/settings & ignores with the monorepo
* Upgrades to the same version of typescript and tsconfig settings as the monorepo
* Upgrades the test runner from karma to web-test-runner
* Upgrades the dev server from es-dev-server to @web/dev-server

web-dev-server.config.js

@@ -0,0 +1,14 @@
+import {legacyPlugin} from '@web/dev-server-legacy';
+
+export default {
+  nodeResolve: true,
+  preserveSymlinks: true,
+  plugins: [
+    legacyPlugin({
+      polyfills: {
+        // Manually imported in index.html file
+        webcomponents: false,
+      },
+    }),
+  ],
+};