add a device to my device list in my Apple account
I am unable to find how to add a device, I can only see how to remove a device.
And i can't see the 'number of days' info which is referenced.
MacBook Air 13″, macOS 13.1
Generally the way to add any Apple device to your AppleID is to sign-in to the AppleID with the device.
Usually that sign-in process will require you to provide a 2FA verification code to “join” your AppleID.
See how you can obtain that code here:
Get a verification code and sign in with two-factor authentication - Apple Support