[lib] Refactor messages queue in DMOpsQueueHandler

Summary:
https://linear.app/comm/issue/ENG-9808/consider-modifying-the-queues-logic-to-be-more-resilient

Depends on D13859

Test Plan: Add entities to the messages queue by calling processDMOps from useProcessDMOperation and verify entities are processed.

Reviewers: tomek, kamil

Reviewed By: tomek

Subscribers: ashoat

Differential Revision: https://phab.comm.dev/D13860