Implemented as part of [ENG-10603](https://linear.app/comm/issue/ENG-10603/biggest-risk-factor-out-code-from-databasequeryexecutor)
The goal is to make `connectionManager` non-static. We first need to convert the methods that use it.
`thread_local SQLiteQueryExecutor instance;` in DatabaseManager works, but it is not clean, but this is going to change in TBD.
Depends on D14731