@jmarkows You were right, and it's the current version on MP, I tried letting it switch automatically on capture and it worked that time. Not honestly entirely sure what I did wrong the first time, maybe forgot to preselect the course(?) but you'd think that it would still follow the localizer(unless that messes it up?).
Dunno, it was my first instrument approach and second flight in the Starship so brain was quite busy. Appreciate the comment though, otherwise I probably would've just assumed it doesn't auto swap being a rather antiquated fully integrated avionics system and been swapping manually for who knows how long.