I don't know how kbin login works and I didn't tested it, but here are my thoughts: the single sign on (like login with google) mostly works using the oauth2 workflow. You can use your favorite search engine and look for a nice wall of text for how it works. But basically the identity server (google) approves that you are who you said you are, and kbin uses an access token, for example a JWT token which includes your user information and the issuer, here Google. Kbin can ask Google for validity of the contents of that token, which kbin can approve against Google. So now you are logged into kbin using Google. This token has an expiration, and after that you have to login again. But since this is very inconvenient, there is also a refresh token. Using this token, google with give you a new valid access token with an expiration from now to whatever, let's say a week. This process happens in the back and is silent, so it works without entering your credentials, if it refreshes before expiration. If you don't login into kbin in that time window, you will probably have to enter your credentials again, because the tokens expired. Keep in mind that this summary is not very accurate since it's very simplified and describes the oauth2 process, not specifically what kbin and google are doing.
I think you want to host a website/an webserver: I would recommend to rent a VM server, nothing expensive, 5$ somewhere. Use Linux, any Linux is fine. If you are a beginner, try using Ubuntu since there are plenty tutorials, guides, questions and answers. You can decide if you want to host your service directly on the Maschine using a builded application (search online for .net core build and host) or using a dedicated docker container on your server. Microsoft provides good resources and boilerplates for both. I personally like the docker way cause it requires less installation and maintenance of the VM server, but if you are unfamiliar, maybe try the direct way. Therefore you will need to install some software, basically you will do what the docker container may already provides, but the application has to be builded and executed anyways. If the application is hosted, you probably want something like an nginx or apache2 server to actually host this application on port 80/443 on your Maschine, then it should be available on the IP of your server. Try searching online for a guide how to sett this up. If you want you can also buy a domain and assign some records directing to your server ip, and you will have an domain name with your service on the internet. Congratulations.
In wie weit würde man dem nachgehen müssen? Wie steht Hetzner denn in "Rechenschaft" dafür?