[Clipboard] Reset snapshot on Write Operation

This change introduces a mechanism to invalidate the snapshot when a
write operation is triggered while the snapshot is active. This ensures
that the next read operation will update the snapshot with the new
value, maintaining data consistency.

Explainer doc:
https://docs.google.com/document/d/1yAJsyoDNuAWv1kJy3Osly8vMsO_3cb2vfzbskpcNBVc

Bug: 388081043
Change-Id: I1bad0b68433bdd8035de7cb0a37acd43fb17af38
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/6385937
Reviewed-by: Dan Clark <daniec@microsoft.com>
Commit-Queue: Tanu Jain <tanujain@microsoft.com>
Reviewed-by: Pranav Modi <pranavmodi@microsoft.com>
Cr-Commit-Position: refs/heads/main@{#1463903}