[lensoverlay] Fix back to page UI bugs.

This fixes:
- Changes close button position and background color to align
with spec.
- Notifies the side panel of a page content update so it can
update whether the searchbox is contextual.

Bug: 428104205, 428106143
Change-Id: I65b7bae1afaed3a4ffbec7301f05780192cde7ce
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6685230
Commit-Queue: Juan Mojica <juanmojica@google.com>
Auto-Submit: Juan Mojica <juanmojica@google.com>
Reviewed-by: Duncan Mercer <mercerd@google.com>
Commit-Queue: Duncan Mercer <mercerd@google.com>
Cr-Commit-Position: refs/heads/main@{#1480655}