[iOS][CodeHealth] Only call Push Notif Client that needs to be used.

This CL adds initial support for Notifications to be opened, and their
interactions handled by the appropriate PushNotificationClient instead
of the previous approach, which would send the notification to all
clients for processing.

This CL maintains the previously working infrastructure, so any
existing clients without this information on the payload can process notifications the old way.

Bug: 366550058
Change-Id: I5e807892aa7fe67291e3d3f28208eeab01e1c7dd
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5861908
Reviewed-by: Scott Yoder <scottyoder@google.com>
Code-Coverage: findit-for-me@appspot.gserviceaccount.com <findit-for-me@appspot.gserviceaccount.com>
Commit-Queue: Guillem Perez <guiperez@google.com>
Cr-Commit-Position: refs/heads/main@{#1360080}