Closes https://github.com/ppy/osu/issues/35721.
I worry that straight up removing the nuke and not adding any channel
leave calls in exchange is going to leave tourney client users
with the *inverse* problem of being joined into a gorillion channels
from multiplayer matches they broadcasted, so this attempts to strike a
reasonable balance.
This was always haphazard code, but by luck it never triggered before
drawable load until now. With the recently nullability changes, this
would be triggered when `flash` is not yet constructed.
Switching to `AddOnce` seems safer to avoid multiple applications,
regardless.
Seems a lot more reliable, and allows falling back to the "main" video
in cases which didn't support this previously.
A next step may be to allow every screen to support a video based on its
screen name, rather than specifying the local `TourneyVideo` every time.