Trying to resolve this problem for a teacher.
red "Gmail is having authentication problems. Some features may not work. Try loggin" alert.
Clearing the cache was suggested.
Checking to see if site settings for gmail had blocked account.google.com cookies. I changed it to allow reading cookies and it worked.
Work in progress:
https://www.digitbin.com/google-mail-requires-cookies-enabled/
https://support.google.com/mail/thread/3487373?hl=en
