[Settings Search] Launch Search in Settings

Bug: 444474790
Change-Id: I265158c17b602c3e5caa922f8f8b7b617c5b52ce
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/7832910
Auto-Submit: Moe Adel <adelm@google.com>
Reviewed-by: Gazal Agarwal <agazal@google.com>
Commit-Queue: Moe Adel <adelm@google.com>
Cr-Commit-Position: refs/heads/main@{#1628059}
NOKEYCHECK=True
GitOrigin-RevId: c8dcdf31601588448e4172254c609da227ddc4cf