The new carousel implementation was lacking some scroll related
behaviours. This makes sure that post-filter, the selection is
re-centered *unless* the user has scrolled away manually.
This matches the old carousel's behaviour. See
https://github.com/ppy/osu/pull/16647 for original implementation.
Closes https://github.com/ppy/osu/issues/33052.
This also fixes code running in `Update` which shouldn't be, by
consuming the new `NewItemsPresented` callback.
Fields and properties are renamed to knock some sense into things (was
previously called two or three different things).