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

tsconfig.json

@@ -1,11 +1,12 @@
 {
   "compilerOptions": {
-    "target": "es2017",
-    "module": "es2015",
-    "lib": ["es2017", "dom", "dom.iterable"],
+    "target": "es2020",
+    "module": "es2020",
+    "lib": ["es2020", "DOM", "DOM.Iterable"],
     "declaration": true,
     "declarationMap": true,
     "sourceMap": true,
+    "inlineSources": true,
     "outDir": "./",
     "rootDir": "./src",
     "strict": true,
@@ -13,6 +14,8 @@
     "noUnusedParameters": true,
     "noImplicitReturns": true,
     "noFallthroughCasesInSwitch": true,
+    "noImplicitAny": true,
+    "noImplicitThis": true,
     "moduleResolution": "node",
     "allowSyntheticDefaultImports": true,
     "experimentalDecorators": true,