[native] Use processDBStoreOperations function everywhere

Summary:
We don't need to use async functions that process a single store. They will be deleted in the next diff.

https://linear.app/comm/issue/ENG-6004/wrap-all-store-operations-from-one-action-in-transaction

Depends on D11921

Test Plan: Checked if persisting drafts still works.

Reviewers: kamil, marcin, varun

Reviewed By: marcin

Subscribers: ashoat

Differential Revision: https://phab.comm.dev/D11922