I literally had a discussion about this staircase in a local writing server back in 2020 (a few months before Rowling decided to stop being a good person). We discussed everything from its utter failure to prevent lesbian relationships, to how many health and safety regulations a staircase like that violates (too many, some kid is going to break their neck!)
Although, now that I'm considering the trans aspect of the enchantment, how does it determine gender anyway? Is it sex-based, or identity based? If the trans person doesn't know that they're trans, will it still trigger? And if it doesn't, then it must be reading their minds or something to figure that out (or going purely off gender expression, in which case, can cross-dressing fool the spell? That seems like a massive oversight...)
Welp, as with most of the HP worldbuilding, the details only leave more questions. I'm half-tempted to say that a spell like could be useful for speeding up the transgender questioning process, but given the complexity of that topic, I have a suspicion that any Magic Stone of Validation would just explode before giving a straight answer :/