[UNOp2][Android] Hook up the new signin flow to the back-of-cards promo

Fixed: 41493781
Change-Id: I389ecf0a058e06db7915b29c912ff6ad42f8be10
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5419196


Reviewed-by: Tanmoy Mollik <triploblastic@google.com>
Reviewed-by: Cathy Li <chili@chromium.org>
Commit-Queue: Samar Chehade-Lepleux <samarchehade@google.com>
Cr-Commit-Position: refs/heads/main@{#1282413}