Hey. I first noticed this on 01/03/25, but it had been on my iPad Mini for probably a few days already. I called Apple Support. Very long phone call, but they were able to verify 1) that this forum post is the only available screen shot (nice work @LotusPilot); and 2)that they don't know what it is either. They helped me troubleshoot some security settings – there were a few unrecognized phone numbers from the EU/K in my 'trusted phone numbers' that I got rid of; but the whole process of screen sharing with the Apple rep solved the situation by replacing the mystery icon with the rep's purple screen share icon. So, they gave me a case ID# and I called it a night.
It showed up again tonight for the first time. I called Apple Support, reopened the case. None of the security infos have changed, but strangely I wasn't allowed to Accept the screen share, but only Reject: twice. Third time I rotated the screen to portrait, and it worked. That, and the fact that it got replaced/annihilated by the screen share icon again, as well as noticing that the mystery icon was both faintly pulsing and impervious to any action or dialogue whatsoever, leads me to agree with @varjak paw (thank you) that it's an exploit designed to sync or share information. However, it doesn't exist at the handy 'status icons meaning'-link provided.
This time I'm going to get a callback tomorrow – they don't have any new infos, but they're looking into it. I'm not optimistic, but at least it goes away after screen sharing with the Apple rep (only known resolution).