I am experiencing what OP describes.
In attempting to import and sync my iCloud calendar and contacts with Outlook 365 for Mac, one needs to use one's iCloud account (AppleID username/password) to create an account in Outlook.
On generating the account in Outlook and using AppleID username and password causes a denial from iCloud and a notice that one needs to create an app-specific password.
Some apps made by developers other than Apple ask you to sign in with your Apple ID, so that the app can access information like mail, contacts, and calendars that you store in iCloud. To help make sure that your Apple ID password can't be stored or collected by the app, you can choose to create an Apple ID password to use only with that app
The problem that OP notes and that I've experienced is the following:
How to generate an app-specific password
- Sign in to appleid.apple.com.
- In the Sign-In and Security section, select App-Specific Passwords.
- Select Generate an app-specific password or select the Add button
, then follow the steps on your screen. - Enter or paste the app-specific password into the password field of the app.
Following the steps above, at STEP 3 an endless loop occurs at the point noted by the OP.
I have two-factor identification on for my MacBook Air Silicon, my iPhone 12 and my Apple Watch 6 and they are all within a foot of each other, all on the same wifi channel. These do not get a pop-up notice which I suspect is that the app-specific password routine is looking for.
I'm as stumped as the OP.
Any ideas?
Thanks