Cannot Get Mail. No password provided for "iCloud".

This is the error I get when I try to check mail on iPhone using the default Apple Mail app.

Never touched a single setting in over a year, never had a problem in over a year. Suddenly, today at around 3AM, Mail app stopped retrieving new mail and started displaying the aforementioned error.

I've tried every possible "solution", you name it:

• Quitting Mail app and relaunching
• Restarting iPhone
• Signing out of iCloud and signing back in
• Resetting network settings
• Resetting iCloud/Apple ID password
• Erasing iPhone and setting up as new

Absolutely nothing solves the issue.

This has affected all my Apple devices: two iPhones, two Macs, two iPads.

However, everything works fine if I access iCloud Mail through a computer browser.

Here's what's even more bizarre:

While trying to solve this issue, I thought why not try to access iCloud Mail through a third-party app, such as Google's official Gmail app?

To do that, I needed to generate an app-specific password through Apple ID website. So I did. However, none of the third-party mail apps I tried accepted the generated app-specific password. I tried several times with several different passwords. I believe that they stopped working around the same time as Apple Mail app stopped retrieving new mail. Something deep within my Apple ID got seriously messed up, which has broken mail retrieval and subsequently app-specific passwords.

But what could have possibly done that??

But more importantly, how do I fix this? 😭

P.S. Please don't suggest Apple's generic "If you can't receive emails on your iPhone" type of support articles. My issue is much more egregious.