The way spectator currently works, the `Spectator` screen is responsible
for adding new frames to the replay, even when it has a child
(`SpectatorPlayer`) present.
There was a possibility that a new play had already started, and on
returning to the Spectator screen (to initialise the new play) there
would be a brief period where the Player instance is still reading from
the replay, the `userBeganPlaying` call had not yet finished
initialising the new target replay, and `userSentFrames` is run
(asynchronously), writing frames to the previous replay using the
incorrect ruleset instance).
To make this work, it doesn't `Schedule` frame addition to the replay
(making things a bit unsafe). Changing this itself isn't such a simple
one to do, so I instead opted to fix this via locking.
Closes https://github.com/ppy/osu/issues/10777.
