Unfortunately that doesn't work either. But if I set the DNS server on the G linet to manual and set Cloudfare (1.1.1.1) or Google public (8.8.8.8) everything runs via VPN. However, with only 5mbit/s. My provider speed is usually 100mbit/s. With DNS automatically there is no connection to the internet. I'm one step closer to solving the problem
That's default behaviour unless you change from global proxy mode. Go to VPN Dashboard and click "Global proxy" change to client based routing and choose what to allow or not allow to route via VPN.
Also I am pretty sure there is a DNS bug somewhere hence why selecting auto mode and or manual gives you the DNS again for the router when then VPN is enabled.
As soon as I set the DNS server to automatic there is no connection to the internet. It makes no difference if I change the proxy mode on the mt300n v2. I'm now contacting cyberghost to see if there is a problem with your VPN configuration.
By the way, you won't see much improvement in regards to speeds with the mt300N-v2 the speed you are getting with OpenVPN are within spec for the hardware. You want to use a wireguard config to get better speeds.