[iOS] Refactor and Centralize Navigation for Background Pickers

This CL refactors and centralizes the navigation logic for the various
background pickers into the
HomeCustomizationBackgroundPickerActionSheetCoordinator. It also
introduces a new delegate protocol to allow background pickers to return
the selected background configuration.

Although the delegate's usage isn't fully implemented yet, this CL sets
up the intended architecture: when a background is selected, it will be
applied immediately. However, the background will only be added to the
"Recently Used" list once the user dismisses the picker. This ensures
that only the final selected background is saved, rather than every
background the user previews.

New experience: Color Picker:
https://screenshot.googleplex.com/3DkuexkGCiJs8Ai

Preset Gallery Picker (small):
https://screenshot.googleplex.com/6EosnheKZTHDU6p

Preset Gallery Picker (expanded):
https://screenshot.googleplex.com/4o5BubrSgy6a4oB

Bug: 408243389
Change-Id: Iae9aab5e915db56bc12f44c9b8fe8013e408ef1a
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6617029
Reviewed-by: Adam Arcaro <adamta@google.com>
Commit-Queue: Pier-Alexandre Bouchard <pabouchard@google.com>
Cr-Commit-Position: refs/heads/main@{#1470523}