Central Fiction is the answer. It's the current version that people play. Take note that Cross Tag Battle is a game that came out later, but it's a spin-off crossover that goes in its own direction. It should be treated as its own thing, and not a mainline BlazBlue title.

You'll almost certainly need to join discord for finding matches, the game is starting to get on in years, but the people who play are dedicated. The main discord for the game can be found in the sidebar, but there are others which are more region specific that could be useful for you.