Man, of all the times to finally introduce Terry, they go with Batgirl.
Would personally rather see Batgirl since she’s actually from the comics. Although Barbara Gordon was merely just okay as Batgirl (she got more interesting as Oracle), Cassandra Cain and Stephanie Brown were better characters as Batgirl due to being an insane badass and fun/lovable respectively. Regardless, seeing any of them will be better than the garbage we got in the 1997 movie.
I like Batman Beyond, but I never felt it should be a thing anywhere else. Bruce pushing his crime fighting family away ultimately is not something I want to see in the other mediums as it would just mean I’m seeing him make the same mistake over and over again (and wouldn’t make sense with Affleck’s Batman right now as he’s all about uniting heroes, he’s not some angry loner). Dick Grayson (who should be out there, as Jason’s existence was already confirmed) should be the true heir to the Bat mantle followed by whichever other Robins or Batgirls there are, and sure enough the comics did exactly that when Bruce vanished for a while and it was actually great, Dick and Damien played off each other really well.
Again, I like Terry, but I don’t really want the movies to tackle that save an alternate reality movie or something as I’d rather they follow the comics more especially since the extended Bat family has to this point been either absent or poorly adapted in the live action films. I mean, Kingpin was the clear biggest villain in the 90’s Spidey cartoon, but thankfully the live-action movies ignored that and followed the comics by putting more emphasis on the Osbornes, Doc Ock, etc.