Implement click and aria-pressed for NTP's Wallpaper Search Button

- Adds click behavior + updates relevant metrics
- Adds aria-pressed behavior

* Hiding the button for users who don't have wallpaper search setting
turned on will happen in another CL.

Click behavior works in tandem with the Customize Chrome button.

User journeys for clicking Wallpaper Search button:
- Side panel is closed -> Opens Wallpaper search
- Side panel is open to non Wallpaper Search page
    -> Opens Wallpaper search
- Side panel is open to Wallpaper Search
    -> Closes side panel

*video demo in bug comment #4*

Change-Id: I6d5ace655e5cda6ad83f44394fa49d8313de7083
Bug: 324631907
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5304132
Reviewed-by: Tibor Goldschwendt <tiborg@chromium.org>
Reviewed-by: Alex Gough <ajgo@chromium.org>
Commit-Queue: Paul Adedeji <pauladedeji@google.com>
Cr-Commit-Position: refs/heads/main@{#1262041}