I have had repeated incidences where I was unable to reach my email for days at a time. Today I am day six of my email being inaccessible on my laptop. Their website doesn't accept the existence of Edge (although their steps for Chrome don't work, so maybe it doesn't matter). Contacting their customer service got me a form letter that basically restated their poor website. I use this email to administer a non-profit, so it leaves us hurting and no one at GMX seems to care.
Recommendation: Get an account elsewhere.
I have been using GMX for about 12 years and never had a glitch, until now. I have encountered the same problem with my laptop that you described. My mobile app works great! I clear the cache, paused my VPN and changed passwords about a half dozen times. It works the first time I log in after a password change, but then takes me directly to the Help splash page on subsequent log-in attempts.