Is it possible to run a sever action that triggers a shortcut on a device which isn’t connected to my iCloud?
Does your “device” have a remote access option such as SSH or a web API, that you can access very a Shortcuts? E.g. Is it a Mac/PC/appliance, or is it a separte iPhone/iPad with no server running to receive any requests?
It would be the iphone of my girlfriend so I could also automate her stuff.
I think in general then the answer would be no.
So theoretically I’d need another iPad and a server for her?
Well she would need something (not exclusively an iPad) to receive and run the unattended automation. It all comes down to what exactly you are trying to do. You were referring to a specific device and now introducing another device, but that won’t run things on the original device; but it may be able to update the device with information if you are using iCloud, which you mentioned, to share information.