I think most (all?) Steam games link steam_api.dll (or something like that) which somehow figures out the running Steam process and thus the Steam ID, and then does a HTTP API request to check that you own the title.

Like 15 years ago Steam launched CEG (Custom Executable Generation) - I remember reading a write-up a while ago, but each user had a customer launcher generated on install I think, and I think there was an extra segment put into the .exe file and that was put to use somehow, though I don't know if CEG is still a thing.

The ownership check you are referring to is a local check. There is another check (involving EncryptedAppTickets) which is not local, but far fewer games use that.

CEG is long dead/was broken immediately in a pragmatic, automatable way.