PrintPreview: Migrate to Lit, part 13.

In this part migrating
 - ui/destination_settings.ts

As part of this migration, had to modify sidebar.ts
`onDestinationChanged_()` logic, to invalidate the previous
`destinationCapabilities` object, so that it isn't erroneously used by
other elements until the next `onDestinationCapabilitiesChanged_()` is
fired, which addressed race conditions that were causing test failures.

Bug: 410607166
Change-Id: I8b1977337986bef794a93fa41e0b23d422a64dbb
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6508408
Reviewed-by: Rebekah Potter <rbpotter@chromium.org>
Auto-Submit: Demetrios Papadopoulos <dpapad@chromium.org>
Commit-Queue: Rebekah Potter <rbpotter@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1457419}