CastFeedback: Migrate to Lit, part 2 (last).

In this part checking in the cast_feedback_ui.html.ts file instead of
auto-generating it, removing the Polymer dependency and fixing
additional type errors due to the stricter TS compiler flags.

Bug: 40943652
Change-Id: I3b004a838f74fc061f44816dbccaa1e11dd16250
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5609753


Commit-Queue: Demetrios Papadopoulos <dpapad@chromium.org>
Reviewed-by: Takumi Fujimoto <takumif@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1313180}