Ah. Gotcha.
I still think that probably clouds WB’s thinking. Studios and their heads can be overly precious about what they think their biggest ticket items are and I wouldn’t be surprised if they wanted The Batman to feel more Oscar-y bait like Joker and maybe the shine would be taken off the character overall by putting him in that TV show.
Also, purely from a story standpoint, with all the trash Peacemaker talked about Batman, if Bats was there, just shrouded in shadows, there would have been no interaction which woulda felt weird. Can’t load that gun all season and then not fire it if Batman actually showed up.