The categories likely have more to do with the structure and running time of the shows. The general rule of thumb is that comedies are a half hour and dramas are an hour.
The Bear is around 30:00/episode (it varies a bit) and is structured like a sitcom: three interwoven stories per episode (with a few exceptions). Succession is 1:00:00 long, and is (probably, I’ve never seen it) structured like a drama, with four interwoven stories per episode. There’s always comedy in drama and vice versa. Lots of stuff in The Bear was funny, and I imagine there were plenty of dramatic moments in Succession.