This weakens security. Now auth tokens can be logged or actively intercepted on corporate networks with TLS MITM and these URLs will eventually find their way into emails and other unencrypted locations. Not exactly progress.
The behaviour with third party cookies blocked is how oauth2 works by design.
Even without third party cookie blocking, if you're at p1.com and you click to log in with a1.com but you're not logged into a1.com yet, you get forwarded to a1.com to sign in.
So with third party cookies blocked, it's no less secure than it was before.
