See https://lemmy.world/comment/9404186 for a Solution. Spoiler: switching from NVIDIA to an AMD GPU fixed the issue.

I just bought a decommissioned computer from a public institution for 40€ (they are usually relatively cheap and still top modern, since companies replace their computers after 2 to 4 years, for tax reasons).
For this I just bought 2 HDD hard drives (I can only put 2 in; they are relatively cheap in comparison for a lot of storage space) and a nvme2 ssd was already included, there is the OS on it.

To make the server publicly accessible with a private internet connection (not a business connection), I bought a domain (I bought it at namecheap) and then I set up DynDNS at my domain provider and my router. This was relatively easy (with namecheap and a FritzBox).

I added a DNS entry that forward all subdomains to my DynDNS. The software, I want to have installed, I then simply install in a docke/ podman container and make a reverse proxy to the docker container via Nginx. This allows me to let multiple applications use the http(s) port from the outside via subdomains, so the URL doesn’t need a port.

I can post the specs later, with an edit.

Edit: I don’t know how much the electricity costs, because I currently don’t pay for the electricity. But I have a 200W Power Supply and the machine is idling around a lot, as the service just not often used, but sporadic.