Apple ID being used on New Apple Watch
This message just appeared on my MacPro
I had not signed into my 'Old' Apple Watch
Should I take any action?
Apple Watch Series 1, watchOS 6
If that is the name of your watch, you are probably okay. I occasionally get messages like that.
Check your device list to see if there is a device signed in that you don't recognize. You can remove the device using the steps in the article below. As a precaution, change your password.
Apple ID device list -Check to see where you‘re signed in.
What to do after you change your Apple ID or password - Apple Support I suggest doing this before you change your Apple ID or password.