[web] handle message store local ops types in processMessageStoreOperations

Summary:
We need to update processMessageStoreOperations to handle the local message operation types

Depends on D12253

Test Plan: Confirmed that when processing message store ops on web we were successfully handling the new local message operation types

Reviewers: will, tomek, kamil

Reviewed By: tomek

Subscribers: ashoat, tomek

Differential Revision: https://phab.comm.dev/D12357