Add Feature Flag to Offstore Extension Trigger

The newest trigger for the extension needs to be gated behind a finch flag for finch testing.

Bug: 322898393
Change-Id: Ic7f7eb27b66ef71bb909960f3164707831e5c6cc
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5428905


Commit-Queue: Adam Psarouthakis <psarouthakis@google.com>
Reviewed-by: Side YILMAZ <sideyilmaz@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1283380}