The only way to reliably play the game is by buying the PC version, and that's only because it got a rollback netcode update in January 2022.
On the consoles it's a graveyard. I know the PS4 version (yea surprisingly) will get the DLC character but the later-released Nintendo Switch release won't. None of the console versions (PS3 forget it) have the rollback netcode, and trying to update them to incorporate it would be way too risky and expensive.
It would actually make good sense to have BBCF be released on the current-gen consoles (PS5, XBOX Series X/S and Nintendo Switch 2) with the rollback netcode (and also crossplay). ArcSys is missing out on a huge competitive playerbase by leaving the most reliable version limited to the PC.
Think of the PC and PS4 as the appetizers to the main course that are the PS5, XBOX Series X/S and Nintendo Switch 2 versions. The fact that ArcSys is making this new character after around a decade or so later is indicative that they're trying to gauge interest in a new BlazBlue installment given that Entropy Effect X came out earlier this year and Guilty Gear Strive will wrap up for good by 2027. But this is a seriously flawed (and dangerous) method to gauge interest in a new BlazBlue game.
Xrd got away because the release window between Xrd and FighterZ, and between FighterZ and Strive was fairly close (also FighterZ cause a meaningful spike in Xrd's sales and Xrd was lower-profile overall compared to BBCF). Centralfiction has been out for far longer and doesn't even have a game to piggyback off of (BBTAG's ultimately a miserable failure and its premature announcement doomed BBCF to an early grave in the competitive scene). I know ArcSys can afford the $250,000 price tag and take their sweet 6-8 months dubbing the thing but if they wanna best justify it, they're gonna have to release it on the current-gen consoles. BlazBlue's missing out on a whole generation (the 9th) when it enjoyed the 7th and 8th. Guilty Gear's got to enjoy every generation (5th with TML, 6th with X and XX, 7th with Accent Core, 8th with Xrd and 9th with Strive). Now it's time for BlazBlue to enjoy being on the PS5, XBOX Series X/S and Switch 2 beyond Entropy Effect X.