Account not authenticated; Re-enter Password does nothing

After Microsoft disabled Basic Authentication on 10/1, some of our iPads & iPhones have a new issue. In Settings/Mail/Accounts/Exchange Server, we get a message "Account not authenticated" with a link to "Re-enter Password". On most devices, touching Re-enter Password opens a prompt to enter the password, authenticate, and approve permissions and email & contacts work again. On about 20% of the devices, "Re-enter Password" will go gray, then back to blue, and the password prompt will not open. Thus, we cannot authenticate or get email/contacts working.

I have tried power cycle, updating to iOS 15.7, removing and reinstalling the Apple mail app, clearing Safari cache, disabling MFA, among other things.

Most of our users have both an iPhone and an iPad. For some, one device works fine, but the other does not. That seems to rule out an account issue.

MFA had been set up earlier with the iPhone phone number, an IT phone number, & the Microsoft authenticator app for authentication, and an app password because Apple Mail required that. Email and contacts were working at that time.