Didn't really work to fix these tests due to the sticky nature of the
failure. Also I can no longer reproduce locally, so the hope is that
these are fixed by https://github.com/ppy/osu/pull/30634.
This also throws away the logic of updating
`API.LocalUser.Value.Statistics`. Components should rely on
`LocalUserStatisticsProvider` instead for proper behaviour and ability
to update on statistics updates.