I opened Keychain Access. (I searched for it).
In Local Items, I deleted all the entries for com.apple.cloudd.deviceidentifier.Production, plus iCloud Keychain Account Meta-data.
After logging out and back in, I think the red dot remained. But, when I went to System Settings, the entry for "Update Apple ID Settings", on the left below "sign in with your apple ID", had gone. Then I noticed the red dot was gone.
It's possible this was a coincidence, and macOS had just fixed the problem itself, a few minutes after the upgrade to 13.2. There was a notification about "optimizing" my computer, and that it would be slower until it had finished. See also: "I've been told confidently it has been addressed in 13.2".
Answer from sourcejedi on Stack Exchangenotifications - How to fix "Update Apple ID Settings" bug, when I don't have an Apple ID? - Ask Different
Update Apple Account Settings | MacRumors Forums
Update Apple ID Settings Loop
“Update Apple Account Settings” : AppleWatch
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AWU2 running watchOS 11. When I go to settings on the watch directly, right underneath my name it says “Update Apple Account Settings”. When I click, it says “Some account services require you to sign in”. The first time it did ask for my Apple ID password and just spun forever. This message continues to stay and now when I click on it, and click continue it just stays on a spinning wheel forever. Tried rebooting both watch and phone and message remains in settings. Any thoughts?
(EDIT/UPDATE: as a few of you have pointed out, watchOS 11.0.1 did NOT resolve the issue as hoped)
(UPDATE 2 : 11.1 also did not resolve this bug. Please report this to Apple so it is hopefully fixed in the next software update)
Been getting this for the last 2-3 weeks. I click on continue, enter my Apple ID password, then it prompts my phone unlock code, then my MacBook password.
Then it loops back to the image on the post. Nothing changed.. it’s an endless loop
Any ideas? As far as I can tell, the only limited feature is that my keychain iCloud has been disabled.