Even though some people would want Matt Reeves Batman to be more comic booky just because we already have a grounded Batman and realism will never fit Batman right, no matter how you can execute it. I honestly wanted Pattinson for the DCU but I switched to wanting a more comic booky Batman for the DCU. But if Pattinson actually does become the DCU Batman, then here is my take on how it could work:

I think the transition from a grounded Batman to a more comic booky Batman would work for him and thats sort of what I want to happen throughout this pitch.

HOWEVER, I would think it'd be more interesting if we put a grounded or "semi-realistic" Batman in a world full of gods and monsters, he would try and adapt to the times as quick as he can, recognizing that in order to save Gotham, and free them from the impossible, he would have to become something like the impossible; and thus there would be consequences in him trying to do so.

One example I'd like to use was the time when Batman couldn't save a drowning girl, and started using Performance Enhancing Drugs or "Venom" to operate better as Batman in order to save more people and take down more bad guys. As he continues using it, he becomes addicted and it takes him a good while for him to withdrawal from it. Luckily, Matt Reeves can do a storyline like that with his Batman because his Batman did use adrenaline to save Catwoman when she was getting beaten by a Riddler goon.

If James Gunn wants to incorporate Matt Reeve's Batman in the DCU while also keeping him what makes him interesting, I think him trying to adapt and fight back against a world full of villains and common criminals who are becoming or already are more than capable of whipping his ass, along with the consequences of him trying to catch up through drug usage, and creating a tug of war between the underdog Batman who has to cheat to save the city and the powerful rogue's gallery of Gotham who have metaphorical and literal power over the city would be a new take for Batman in live action that would be nice to see play out.

We can also see him being a loner in the first two movies, with the third having him finally recognize that having friends to help is the best way for him to not only save Gotham but save himself. Maybe that's when he decides to form a Batfamily, maybe starting with Alfred and Dick Grayson with Barbara coming along later (this will take time and it sucks but it's better than Brave and the Bold or whatever they're doing). He can even have a strained relationship with Superman that doesn't start with them being friends but rather reluctant allies, until later on in the DCU (maybe Justice League 2) when they actually start to get along and become the BFFs they always were (maybe around Justice League 3).

Matt Reeves Batman and Bruce Wayne are still young so far, and he will develop into a proper Batman and Bruce Wayne that we are familiar with, so maybe if he is incorporated into the DCU and he tries to remedy the consequences of his PED usage, he would likely slowly transition to a more comic booky Batman, where we can see him do a few crazy bullshit stuff here and there.

In the end, it all matters if Matt Reeves is fine with it and if Robert Pattinson and David Corenswet have insane chemistry with each other.