Besides the MAC lookup suggestion, have you tried to simply find hostname in local DNS by reverse IP lookup, maybe that would shed some light.
Not sure if there is anything useful, but in browser just check site source, maybe there is something useful there that could help with identification. Does site have certificate? It might include info that would help with identification. Do the standard browser network trace via dev tools F12, maybe something useful appears there.
In nmap you can attempt to guess OS, try that. Additionally it might be possible to get hostname as well.
And have you checked your router to see if this connection is connected to your Wi-Fi AP or Ethernet to narrow things down? If it is not possible to determine this from router, simply connect your main PC to Ethernet, disable AP in router settings and check if IIS site is still up. If it is not, enable AP again, does it come back early or it takes some time?
Lastly, if it still is a mystery, start powering off devices one by one to find the source. Based on comments it seems you have multiple devices, but I assume it would not take that long?
Aren’t all search queries available to whoever hosts an instance? In my eyes this is much worse to privacy and a much bigger risk unless you really know who is behind your chosen instance. I would trust some a company a bit more with safeguarding this information so it does not leak to some random guy.