I don't think that Burst is Fire/Fairy, because all of the other Ultra Beasts, except Xurkitree, have double weaknesses.
Celesteela doesn't.
I don't really think they'd make it so all UBs have double weaknesses (Celesteela kinda proves that, and if they really wanted to fit that pattern then Xurkitree would have another type slapped on to give it a 4x Ground weakness), even for GameFreak's standards that's a very specific (and borderline unnecessary tbh) thing to have a group of Pokemon to have.