Samesite won't break it if you set it none. Eg samesite=none Google failed to set it before the official rollout.
Reason is that sso effectively uses an iframe or popup to a 3rd party auth provider (Google, Microsoft, Auth0...) Provider saves a cookie with that state (from something like accounts.google.com) and usually reads it back from first party context.
If samesite is not set to none, supporting browsers are not allowed to write cookies on the auth domain from the firstparty context, and so the firstparty scripts don't think it ever happened, even though it did. First party scripts can't read it and so sso failed.
Reason is that sso effectively uses an iframe or popup to a 3rd party auth provider (Google, Microsoft, Auth0...) Provider saves a cookie with that state (from something like accounts.google.com) and usually reads it back from first party context.
If samesite is not set to none, supporting browsers are not allowed to write cookies on the auth domain from the firstparty context, and so the firstparty scripts don't think it ever happened, even though it did. First party scripts can't read it and so sso failed.