If this were a tool for property managers to use only publicly available and internal information to set prices, it would probably be legal.
I don’t see why the data makes much of a difference.
What does make a difference is that the software is interested in benefiting all of its clients simultaneously, even if it ends up hurting a particular client by telling them to not rent an apartment (or to wait for a higher rent). That is the definition of collusion. (Everyone working based on self interest == competition, usually. Everyone working for a common interest == collusion.)
