Change ExecuteRemoteFn to use weak_ptr instead of base::Unretained

Bug: 332592716
Change-Id: I6d5323913d5785d619bed56b85cdb42e2a8cd1a7
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5421869


Reviewed-by: Scott Violet <sky@chromium.org>
Commit-Queue: Sophie Chang <sophiechang@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1283150}