Terry has more of reason to be there than Cloud from Final fantasy 7 does. After that happened I think hey threw out the whole "this character needs to be well established on nintendo systems" thing. I wouldn't be surprised if we got Dante from the Devil may cry series at this point. Nintendo Vs. CAPCOM coming fall 2022.
Cloud was at least in a Kingdom Hearts game on a Nintendo system, but yeah, he's not associated with Nintendo in general. The difference is, though, that Cloud is a much more recognizable character than Terry. He's in because he's arguably the most recognizable character from Square, which is one of the major publishers in the industry.
Besides Bayonetta, the characters they took from third parties are the most iconic ones. Mega Man and Ryu from Capcom, Sonic from SEGA, Pac-Man from Namco. Bayonetta is an exception because Nintendo actually funded and published Bayonetta 2, even though SEGA still owns the license.