[infra] Fix flaky ts-starter-kit tests (#3157)

I think the flakes we have been seeing from the starter kit test were just timeouts. Since things are running in parallel, it sometimes takes longer for browser tests to start. The starter kits now run separately, after the other tests, so that they have less resource contention. We could also bump the `browserStartTimeout`, but since it's a user template repo, that seems weird.

Also:

- Upgrades dependencies
- Removes some unnecessary devDeps from virtualizer
- Adds a changelog entry from #3132 that I forgot (unrelated, just throwing it in)

.changeset/eight-clocks-help.md

@@ -0,0 +1,2 @@
+---
+---

.changeset/three-hounds-rush.md

@@ -7,6 +7,7 @@
 '@lit-labs/task': patch
 'lit-element': patch
 'lit-html': patch
+'lit': patch
 '@lit/reactive-element': patch
 ---