Hmm... Well, according to this, utterly smashing a barrel is worth this much:
https://vsbattles.fandom.com/wiki/References_for_Common_Feats#Destroying_a_Barrel
The results would be different from, say, slicing a barrel in half, but we'll be going off what we got.
Baldi's scaling is a little iffy. According to the wiki, one-shotting someone is around 5x (at least last I checked) AP. Could be less as far as I know, but nobody in the real world was ever brave enough to test that out. Going off 1st Prize as a baseline, this is what I can guess.
1st Prize (base): 18.32 kJ
Gotta Sweep: ~36.6 kJ (probably the highest he can be from pushing against 1st Prize)
Baldi: ~183 kJ (one-shotting the player, who can survive Gotta Sweep without injury)
Aya is about 780 kJ fromthe barrel feat and can hurt herself, so she had that in both AP and durability.
Baldi is significantly faster than Aya, with Baldi having a travel speed rating of 14.2 m/s. His hand can move upwards 29.2 m/s with his ruler slaps, which are done just by rotating his wrist. Aya's speed isn't calculated, but I'll be fair and assume baseline athletic human speed unless if it can be proven otherwise, which is 7.7 m/s.
Baldi's Basics Birthday Bash shows that Baldi can, in fact, use Illusion Manipulation since he both prevents the player from using any exit other than the cafeteria AND shuts Final Mode (where the school goes completely red) off in order to surprise the player. His spatial manipulation is still as questionable as it was in the original game, though. His hearing means Aya's automatically marked for just opening a door.
I'm gonna say this match is
Inconclusive because there is no way Baldi can feasibly hurt Aya with her durability and there is no feasible way Aya can hit Baldi with his speed.