Superman’s entire approach (full sci-fi/fantasy in a world of established heroes) is directly at odds with everything Reeves has said about his Batman (grounded, grounded, grounded), so I don’t think Gunn is angling for Pattinson to be in the DCU as much as he’s just kind of kicking the DCU Batman can down the road a bit.
It’s hard enough just to bring Batman to the screen without the added challenge of having him right alongside another take on Batman that’s already successful. I say hold off a bit, let Reeves do his thing, focus on building out Superman’s corner of the universe/bringing back Wonder Woman/etc. Bide your time with Gotham-set, Batman-adjacent projects (Clayface, the animated Dynamic Duo, the potential Cregger film) and pave the way for his eventual debut. At the moment, I believe Batman is the one character from the Big Two who could actually support that kind of strategy (parting shot at Sony).
But I think audiences are overdue for an all-ages Batman take in the same model as what we just saw with Superman. Nolan and Reeves did their dark, grounded thing, Todd Phillips’s Joker was barely palatable for anyone, and the Snyder/Affleck take botched what should’ve been an all-ages superhero Batman. Let’s make good on that premise.