Breathedge has enjoyed a great deal of success so far after releasing onto the PC and so it is no surprise that fans on the consoles are hoping to see a Breathedge PS4 & Xbox One release some time in the future.
At this moment in time it would appear that there are no current plans to release a Breathedge PS4 or Xbox One version as the studio seem to be focused mainly on the PC.
There has been no official word from the studio regarding a PS4 or Xbox One release and so with the game already released fully onto the PC it seems unlikely.
There have in the past been some games that have released onto the PS4 and Xbox One from Steam such as Ark Survival Evolved and 7 Days To Die but it would appear that Sony are a lot more strict when it comes to certain games releasing onto their platforms which is a shame for fans of smaller early access games.
A Breathedge PS4 & Xbox One release is certainly not out of the question but for the meanwhile if you are waiting for imminent news of its arrival you might be better off getting it on a different platform.