Apart from Michael Gough and Pat Hingle everything else is so different and inconsistent.
It was kinda like a early attempt at a reboot which weren't commonplace until Batman Begins.
It was a continuation but the first four Batman films are for the most part standalone films kind of like James Bond (well except for the Craig films). They may have some loose references to each other but for the most part they do not have a continuing storyline, each film is just its own separate thing.
shareInstead of looking at it as a 4 movie saga, I look at it as 2 pairs of movies.
The Burton/Keaton pair are definitely direct sequels. The tone and look of them are the same. Many of the same characters return, and the Batmobile and Bat Cave are the same. It even makes two references to Vicki Vale, and explains her absence.
The Schumacher pair: With the exception of Batman, most of the characters continue thru the movies. Much more kid friendly movies, with a very comic book style to them.
I wonder if Batman Forever takes place in Earth-95 if the two Tim Burton movies with Michael Keaton take place in Earth-89:
https://www.denofgeek.com/us/tv/dc-entertainment/284856/crisis-on-infinite-earths-earth-89-alexander-knox-batman
https://arrow.fandom.com/wiki/Batman_(Earth-89)
https://dc.fandom.com/wiki/Earth-89
https://www.newsweek.com/crisis-infinite-earths-explained-robert-wuhl-alexander-knox-batman-earth-89-1476174
https://fullcirclecinema.com/2019/10/11/crisis-on-infinite-earths-michael-keaton-batman/