It shouldn't. "Exceptions are made for cross-site cookies when they're needed for non-tracking purposes, such as those used by popular third-party login providers."[1]
Probably yes, but it shouldn't be difficult to get an exception by posting a request to the Firefox bug tracker. In the meantime users can disable Enhanced Tracking Protection on the specific site with the new SSO provider.
[1] https://blog.mozilla.org/security/2021/02/23/total-cookie-pr...