Apple ID Sign-In: "Unknown Error Occurred" when trying to sign on Safari

I've been facing a persistent problem with my iCloud account for years. While my Apple ID works seamlessly on my iPhone, logging in through Safari on my MacBook is impossible. Every attempt results in a message instructing me to verify my Apple ID, followed by an "Unknown Error Occurred" alert. This issue extends to my Apple Fitness social features, where I am unable to receive, accept, or send invites.

I have cleared the browser cache, ensured that my macOS is up to date (currently on Sonoma 14.4.1), and I am using an M2 MacBook Air. Despite these efforts, which include signing out, multiple phone restorations with and without backup, the issue remains unresolved.

Is anyone else facing similar issues with their Apple ID, particularly on a MacBook using Safari? Has anyone successfully resolved a similar problem or has suggestions to fix it? I would greatly appreciate any insights and assistance. Thank you.