New Mac won’t accept my Apple Account password

I bought a new Mac Mini M4 (2024) and, while setting it up following all the prompts and instructions, I got to the point where I was invited to add the new computer to my Apple Account so that it would be registered to this single account along with my iPhone and iPad. This step was being done via a log-in field in the System Settings (not via a web browser). Although my email and password were correct, I was unable to sign in this way. I kept being told my password was incorrect. I then used the Forgot Password button to re-set my password (via an emailed link) and was told I had successfully re-set my password. But I still couldn’t log in via System Settings using the new password, although I had no problem logging in via Apple’s website from Safari. I could also log in with the new password via my iPhone’s Settings and my iPad’s Settings.

I contacted the Apple Support team, but they couldn’t work out what the problem was and escalated it, telling me I would receive a phone call the following day and that I would be guided into re-booting the Mac in safe mode.

In the meantime, however, I found a solution by accident. While exploring all the other systems settings on offer, I got down to the iCloud icon, which is quite far down in the Settings list. I was offered a log-in field for iCloud, so tried that, and my password was accepted! Once logged in, my new Mac immediately got added to my account and all my data transferred over. My Apple account now shows all three of my devices.

I am relating this in case it helps others.