Closes https://github.com/ppy/osu/issues/12731.
I haven't tested this, but quite confident it should work. Will test
later today unless someone else beats me.
This is a bit of an unfortunate edge case where the unbind-on-disposal
doesn't help, since the binding is happening in BDL, and the usage is in
a nested `LoadComponentAsync` call. Combine those and you have a recipe
for disaster.