I didn’t want to make the main site unreachable. But I just tried this experiment on our test server and confirmed that you can only sign in using the SiteURL server name. I changed it to the longer name in the config and restarted and then I was unable to sign in using the short name.
I am sure that this used to work… we set things up to work with both server names quite early on for this reason and did the work to sign the certificate properly, etc. I am not sure when it stopped working.