Introduce fork-safety fix to `SessionFlusher` and `BackgroundWorker`

Related:

* getsentry/sentry-python#6149
* getsentry/sentry-python#6148

There have been a couple of reported cases where a deadlock occurs when `os.fork` is used and the child process inherits an acquired lock that the parent process had set.

There are other sites that have a similar code pattern to the issues linked above within `SessionFlusher` and `BackgroundWorker` that will need to be updated to prevent this deadlock from happening.