Issue: Third party cookie access required for login with native account?

For a while now, I have been finding it difficult to log in to hooktheory (via main page) and hookpad webapp (via login popup) with modern web tracking prevention measures enabled.
Using Edge, as this is my “soft” browser for better running PWAs, etc.

Now I’ve had some time to test it, I have narrowed this down to disallowing third party cookie access. Enabling third party cookie access allows login. Turn it off, I’m redirected to an error 400 page at login.

I suspect this is to do with the apple/google third party login integration, but why would the login form rely on the third-party login integration even when it is not being used?
I would think logging in with a native hookpad account should be possible with what is a fairly common, modern browser feature enabled.

Is this intended behaviour?