How to log in to iCloud for iWatch

Environment: iWatch 5 GPS + Cellular, iPhone 11 Pro Version 13.5.1 and iMac 27 inch, 2020 with Catalina 10.15.7

I have previously used my iWatch to unlock my iMac. I had to change the password for the iCloud account shared by all these devices. The iWatch no longer unlocks the iMac.

On the iMac, going to System Preferences / Security & Privacy and then selecting the "Allow your Apple Watch to unlock your Mac" yields a message saying "Your Apple Watch must be signed in to iCloud to allow it to unlock your Mac. You can sign in using the Apple Watch app on your iPhone".

What steps should be taken to sign in to the iCloud account with the changed password?

Thanks in advance for your help!