I would figure the next game to get a TV show would be a SEGA title.
A bunch of SEGA brands have been in talks for a while, and SEGA has been actively shopping its brands around recently. (And by "SEGA", I also mean Atlus titles, as those have also been in discussion,
with even a Persona adaptation on the table.) Assuming the God of War or Horizon shows don't get through development fast, I feel like one of those SEGA brands is bound to get though the development-hell gautlet.
Streets of Rage is already being made as a movie, as
are Space Channel 5 and Comix Zone (albeit the company trying to do those has to count its returns on their Borderlands movie first...) Years back,
SEGA was trying to get adaptations going of Altered Beast, Golden Axe, Crazy Taxi, Shinobi and others, maybe one of those projects is still warm. They already did Shenmue as an anime, and there are Yakuza movies... Wonder Boy has weirdly been one of their the most active franchises but that's not really "theirs" and those rights are complicated and there's no TV show there anyway....
I'm actually going to zag here and randomly say AfterBurner could/should be a show. It's getting a little late to swoop into the Top Gun Maverick slipstream, but pilots, jet planes, big guns, and speed could make for a killer weekly show.
Actually, we already know the next game to get a show: it'll be Knuckles, which will be on Paramount Plus on the 26th. (...But that's cheating.)