Move searchbox button labels out of the NTP directory.

Bug: b:328293795, 328827188
Change-Id: I6178daa71c5473cfaa6aecaf4824d7e4049157b4
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5411237


Reviewed-by: Moe Ahmadi <mahmadi@chromium.org>
Commit-Queue: Justin Donnelly <jdonnelly@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1281235}