Login.gov absolutely cares about your identity. Case in point: login.gov will share your SSN to the provider(irs.gov in this case), if appropriate permissions are requested.
Last time I tried to do something at the IRS website, I had to turn on my camera and have my face compared to the face they have on file to proceed. I don't think login.gov has that level of verification. Whether the IRS needs that level of verification is another question.
That's ID.me and login.gov works differently, but it does absolutely care about identity, they have multiple levels of identity permissions, one of them is , this person has a login.gov account. One of them includes an SSN #.
When does it ask for your identity? I just signed up and all it needed was my email, password, and my token. It doesn’t know who I am though. It didn’t even ask for my name.