My Nespresso App get’s stuck at loading screen a very long time, and ultimately end up with an error saying there is a temporary error.

This behavior can occur if you have a VPN installed/active on the phone.
You can check this in the drop down panel on the iPhone.  It will show the VPN icon next to the network/wifi icons on the top.
VPN can be switched off using through the Settings -> VPN.
Some users might have a separate VPN installed, if so, you can also switch it off through that app.
Should the issue still not be resolved, or you have no VPN active, please try to delete and then reinstall the Nespresso app