> use our single company identity we use for every single service for SSH as well
How would that even work? Do you open your browser, log in, and then somehow transfer the session into your ssh client in a terminal? Does the browser assimilate the terminal?
And let me remind you, HTTP authentication isn't a login form. It's the browser built-in "HTTP username + password" form and its cousins. We're talking HTTP 401. The only places this is widely used is API bearer tokens and NTLM/Kerberos SSO.
> Before initiating a session, users will have to authorise to the IdP, which probably includes MFA or Passkeys anyway. No need for PAM anymore at all.
Unfortunately I need to pop your bubble, PAM also does session setup, you'd still need it. And the other thing here is — you're solving your problem. Hard-relying on HTTP auth for this SSH successor needs to solve everyone's problem. And it's an incredibly bad fit for a whole bunch of things.
Coincidentally, SSH's mechanisms are also an incredibly bad fit; password authentication is in there as a "hard" feature; it's not an interactive dialog and you can't do password+TOTP there either. For that you need keyboard-interactive auth, which I'm not sure but feels like it was bolted on afterwards to fix this. Going with HTTP auth would probably repeat history quite exactly here, with at some point something else getting bolted to the side…