Kuudere-HimeI think one of the first Anime one should look to for how to make a Batman Anime is Kara no Kyoukai.
In YGG Studio's first video on Kara no Kyokai he talked about how the first film does a great job at giving the city personality. And that is something Batman stories always try to do with Gotham, which Nerdwriter did a video on., YMMV on their successes and failures.
Many fans lament how post No Man's Land Gotham isn't really "Gothic" anymore, but rather a more realistically modern city. But that is I feel a superficial definition of what Gothic means. Yes Gothic originally refereed to a style of late medieval European architecture, Gothic Romance however as a genre moved beyond that. Tyler Tichelaar likes to talk about how the origins of modern Urban fiction are tied to moving the tropes of Gothic Romance to a then contemporary setting.
And so perhaps giving a Gothic personality to a truly modern urban environment is exactly where Anime like Kara no Kyoukai and other Light Novels Trixie would call Faust style Light Novels, are more successful then a lot of post No Man's Land Batman stories.