[Android] Launch new sign-in flow from settings

Bug: 41493772
Change-Id: Ibcbfc72e75038931d665164fad5414a6cb6e5927
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5400800


Auto-Submit: Tanmoy Mollik <triploblastic@google.com>
Reviewed-by: Boris Sazonov <bsazonov@chromium.org>
Commit-Queue: Tanmoy Mollik <triploblastic@google.com>
Cr-Commit-Position: refs/heads/main@{#1283065}