[lib][native] unify DBOpsHandler usage

Summary:
Cleanup after enabling DB for all users and after SQLite API was implemented.

Depends on D13108

Test Plan: Play with app and make sure ops are processed and results are persisted.

Reviewers: tomek, inka

Reviewed By: tomek

Subscribers: ashoat

Differential Revision: https://phab.comm.dev/D13109