Until now, the `RealmContextFactory` would be disposed as part of the
drawable hierarchy. This is too early, as it may be being used by higher
level components (like `ConfigManager`s, see #15115) that perform final
operations after the drawables have been disposed.
Seems to make sense moving this out of the drawable hierarchy and in
line with how we were doing things with EF.
Due to the lack of locking, there was a chance the the update thread
`context` was retrieved just before the `flushContexts` call, followed
by `.Refresh()` being run while the blocking behaviour was invoked.
This can be seen in test failures such as
https://ci.appveyor.com/project/peppy/osu/builds/39859786/tests.
As an aside, I tried multiple different methods to avoid `lock()` on the
update thread but they felt flaky. The overhead of lock when there's no
contention is reportedly around 30-50ns, so likely not of concern. We
can address it at a later point if it becomes one.