I can't imagine Reeves' Batman being connected. His movies were even more grounded than Nolan's. I can't see his Batman fighting monsters or aliens. They will probably just be their own thing.
The Reeves Batman and the Joker solo projects make money. They aren't going to go away. I'm sure WB is just going to let them do what they want in their corners while Gunn tries to set up this bigger universe. Sure, there are going to be 3 Batmans and 3 Jokers running around in different projects, which is terrible when you actively want to try and create a large shared universe, but I doubt they are going to abandon or hamper the movies they know make money.
It's part of why I don't think this shared movie universe for DC will ever work. At least not this version. Maybe once all this runs its course and they actually get to start fresh from the beginning it can work, but you kind of only really get one shot to set things up where these characters meet on screen for the first time and WB and Snyder kind of botched it. I'm sure WB/DC will have their movie successes because DC has a lot of valuable IPs, the Joker movie is a perfect example, but to have a successful universe you need to have the fans buy in. For them to feel invested, and I don't really see that happening. The fandom feels so fractured, there doesn't seem to be a ton of confidence, and so many of the projects feel so scattershot. Sure, a Blue Beetle, Lobo, or a Mister Terrific movie will be fun but you need those pillars to hold everything together and I don't know if these confusing versions of Batman, Superman, and the JL can be that.