I've been practicing handstands for quite some years now without any wrist problems. Until a year ago, I didn't do much wrist prep. During the last year, I did occasional first knucke pushups and wrist pushups (but not very consistently).
In July some wrist pain started; taking a break did not seem to help, so I got an MRI, which showed an inflamed tendon. As I kept taking a break, this seems to be healed now, and the type of pain changed. It's now more around the head of the ulna and seems to be mainly triggered by rotation (which is a bit strange, as rotation of the palm is actually done in the elbow).
When seeing the doctor again, the diagnosis was, that it's hypermobility; as I understood it, the ligaments around the carpal bones are not tight enough, so when I put the wrist in more extreme angles (like in a handstand), these bones are not held in place correctly, leading to pain.
Does anybody here have experience with this?