I have had the same problem since getting the car. I can connect to the WiFi in the car but it says "Connected No internet"
The service provider Deutsche Telekom has determined that all is working from their end. They say it is Mercedes problem. Have taken it to 2 Mercedes dealers. They confirm the problem but have no fix.
Have contacted both Deutsche Telekom and Mercedes support. They seem to blame each other.
I did a test:
1) I was subscribed to Deutsche Telekom and tried using the browser in the MBUX it did connect to the internet and I could browse.
2) I unsubscribed from Deutsche Telekom and tried using the browser in the MBUX it did not contact the internet.
3) I re-subscribed to Deutsche Telekom and tried using the browser in the MBUX it did connect to the internet and I could browse.
That convinces me that the problem is that Mercedes do not connect the Deutsche Telecom service to the WiFi but only to the MBUX browser.
I have not found a way to contact the engineers at Mercedes to report the problem.
They need a feedback reporting method. I have other problems that may be more of a safety concern I would like to report.