[M123] Change NTP Wallpaper Search button's visibility logic

Changes wallpaper search button's setting observer logic so that it only hides the button, does not show it. This prevents the button from showing if Wallpaper Search's enablement logic changed since the NTP loaded, and has somehow diverged from Customize Chrome's.

(cherry picked from commit 30139ce7ad2b4fa8c613a7d04d5e54d05a797d99)

Change-Id: Iba4867adee740d98b0af320ea77ea4619d5cab01
Bug: 328085545
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5353693
Reviewed-by: Riley Tatum <rtatum@google.com>
Commit-Queue: Paul Adedeji <pauladedeji@google.com>
Auto-Submit: Paul Adedeji <pauladedeji@google.com>
Commit-Queue: Riley Tatum <rtatum@google.com>
Cr-Original-Commit-Position: refs/heads/main@{#1269882}
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5363752
Commit-Queue: Rubber Stamper <rubber-stamper@appspot.gserviceaccount.com>
Bot-Commit: Rubber Stamper <rubber-stamper@appspot.gserviceaccount.com>
Cr-Commit-Position: refs/branch-heads/6312@{#532}
Cr-Branched-From: 6711dcdae48edaf98cbc6964f90fac85b7d9986e-refs/heads/main@{#1262506}

• chrome/browser/resources/new_tab_page/app.ts[diff]
• chrome/browser/ui/webui/side_panel/customize_chrome/wallpaper_search/wallpaper_search_interactive_uitest.cc[diff]
• chrome/test/data/webui/new_tab_page/app_test.ts[diff]