[UNOp2][Android] Hook up the new signin flow to the recent tabs promo

This CL constitutes the initial plumbing for the recent tabs
integration. In a follow-up CL, logic will be added to sign the user out
when they decline history sync.

Bug: b/41493774
Change-Id: I138c3e6665f40bcc148f17d9ee452071f61c602d
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5391318


Reviewed-by: Boris Sazonov <bsazonov@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1281966}