This is one of the most confusing aspects for me when it comes to wallets in general and why I go with cold storage and don't mess around with any of my active addresses. Would much rather make a mistake on non-used address than the other, that could be catastrophic.
You could always stake a separate address for things like proving your identity and never use it for transacting in Bitcoin if you are concerned with your ability to manage your keys. Never sharing your private key is a pretty simple rule though. I would make sure the compromised key is no longer in your wallet to avoid any potential catastrophes if I were you.
I'm Robi12 and I can sign a message.
Lies!
Hello! Why didn't I get the merit? Did I do something wrong?
Address: bc1qu8zggr9cz2z4sjyd0nsxxrm58y90xehadmlx0y
Message: I’m tall3r and I can sign a message.
Signature: HyoqfPzblw+ysSEV8J/gH0d2nsP4M3Onh7/P/1fCpP61TuggEihHm8aCSv8pYPV5+c+0z2QLCojay+SVcLIJqjg=