Closes https://github.com/ppy/osu/issues/30163.
If I'm to be blunt, the decoupled stuff in song select makes my head
spin. I spent a solid 20 minutes thinking how I was going to fix this
one but then finally realised that generally most of the cause there
was the fact that `AdvancedStats` was seeing the new rulesets *before*
the "ensure global selected mods are valid for current ruleset" logic,
and so decided to just _delay_ that until the decoupled transfer
thingamajig happens.
I was honestly considering combining `BeatmapInfo`, `Ruleset`, and
`Mods` into one property on `AdvancedStats`. I figured I'd rather not
push my luck and try the baseline version first, but I honestly think
that direction is going to be required at some point to properly corral
all of the decoupled madness taking place in song select.
