It is a bit simpler than that (the term 'base' can be a bit of a minefield!)
Post Brexit, EU carriers are no longer permitted to operate UK domestic sectors, so these have to be flown using a UK AOC. Emerald operates Dublin-UK under their Irish AOC and will fly Belfast-other UK airports using their UK AOC. Same with Aer Lingus who are now flying Belfast-UK mainland under their UK AOC (albeit using wet-leased BA A320s)