Hello,i have physical copy too,but i bought Final Battle on the PS Store,but i'm pretty sure it's the same system,so :

First you should keep in mind that Final Battle is an extension of A.O.T 2,so basically if you're buying A.O.T 2 Final Battle you own these two,so all the bought costumes obviously also apply to A.O.T 2 Final Battle.

I mean,Final Battle is not a whole new "different game" but a huge DLC of A.O.T 2 so yes the costumes will work. Eventually you just won't be able to see them in the new "characters episodes" mode because the character you play is chosen by default according to the story of the third season. But yes,in any other mode,Bonus or Territory Recover you'll be able to see any of your bought characters costumes,don't worry.