The only way this is possible is for the company itself to run their own friends list servers and do the matchmaking themselves. Notice that Marvel does not have cross play because they just use the Xbox/PSN/Steam friends lists directly, not a “CFN ID” like SFV does. Also notice that SFV’s servers are frequently down and terrible, because Capcom has to maintain them themselves.
Also note that Rocket League, a game with something like 30 million lifetime players, also doesn’t have party/friends list systems because they handle invites directly through the individual platforms. (Although, they announced this is changing early next year)
KI uses Xbox gamertags for their matchmaking, so everything is tied to the Xbox architecture. Unless they wanted to gut the whole system and recode their own friends lists (which is undoubtedly a huge amount of work), this won’t be possible.
This is why my suggestion of assigning a 4-digit code to the lobbies would work. Effectively it’s a temporary username for the players in that lobby, which lets people find each other without having to maintain permanent friends lists unique to this game. You just say “I want to play with player A7T4 right now”, and another player on a different system signed up to be A7T4 a minute or two earlier. Then once the lobby is done, that name disappears.
(My guess as to why there is no ranked crossplay is similar; they have to maintain a leaderboard which means basically having a joined list of all the usernames on both Xbox and Steam, and I imagine there is a large technical challenge in this. It is much easier to get individual sessions to talk to each other, hence the lobby/exhibition crossplay, than it is to unify the architectures of Steam/Xbox to do a joint ranked leaderboard.)