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

docs-src/_includes/nav.11ty.cjs

@@ -1,6 +1,6 @@
 const relative = require('./relative-path.cjs');
 
-module.exports = function({page}) {
+module.exports = function ({page}) {
   return `
 <nav>
   <a href="${relative(page.url, '/')}">Home</a>