Four days ago, I updated my MacBook Pro from macOS Ventura to Sonoma. Since then I've encountered several bugs. This morning, for no apparent reason, Sonoma System Settings decided to show me the warning, "Verify Your Recovery Key".

The warning includes some very scary text:
To avoid losing access to your account, verify your recovery key.
The text is unfortunately ambiguous: it doesn't say why you would lose access to your account. One possible interpretation is that if you lose your recovery key, then you won't be able to recover your Apple ID if it needs recovery. That would make this warning nonurgent, nonessential, paternalistic, and unnecessarily alarming. I know that my recovery key is stored in several secure locations, but any case I've never had to recover my Apple ID in the first place.
Another possible interpretation of the warning text is that Apple will take away your Apple ID if you don't verify your recovery key. This sounds harsh, but… who knows? Apple has neglected to explain the meaning of the warning or why it suddenly appears.
This is not the first time I've seen Verify Your Recovery Key. I actually saw it on my iPad way back in July 2023 after updating from iPadOS 17 beta 3 to beta 4, and in fact the warning still appears on my iPad today.

On July 25, 2023, I filed a Feedback with Apple, "iPadOS 17 beta 4 wants me to Verify Your Recovery Key" (FB12749748). The ultimate "Resolution" of that Feedback was "Investigation complete - Unable to diagnose with current information". Note that Apple never requested additional information from me.
A couple months later, after the release of macOS Sonoma, I noticed the same warning on my Mac mini, and I filed another Feedback, "Sonoma wants me to Verify Your Recovery Key" (FB13215060) on September 29, 2023. That Feedback remains open, with no updates.
I never tried to verify my recovery key on my Mac mini or my iPad, because I don't have my recovery key stored on my Mac mini or my iPad, and frankly, I was worried that the warning is some kind of bug that would ironically make me lose access to my Apple ID or reset my recovery key if I tried to "verify" it.
When I mentioned this issue on Mastodon, someone told me that they've seen the same warning, and verified their recovery key, but the warning eventually comes back anyway. Multiple times! It seems that there's no way to make the warning go away permanently.
I can just ignore the warning inside System Settings on my MacBook Pro, as I've been doing for months on my other devices, but the worst part about the bug is that it badges the Settings app icon, on both Mac and iPad. That I can't ignore, because System Settings is in my Dock.