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Not sure (that's why I don't make a full comment), but I guess that's because the room of requirement is not on the same plan as the school. It kinda exist either elsewhere and the door is just a portal, or in another parallel world. That would also explain why it takes exactly the form and the content needed.
I know that's it's quite common in series to put the same birthday for the character and the actor - hence Grimm with the two main characters sharing their birthdays with their actors. I don't know for sure for Picard though, but I think it's more a nice reference than a coincidence :)