> How could I reliably tell if I'm behind a CGNAT or not? If I poll one of those "what is my IP" websites, and the IP my router has assigned from the wan matches the what is my IP then I'm fine, I'm not behind one, right?

My layman understanding is that the WAN IP on your router will match the "what is my ip" website, but the problem is that it will also match many other people's routers.

Basically imagine your home router and NAT has been moved into the ISP and is serving thousands of end users as well as you... you can't just configure the ISP's CGNAT to forward port 80 to you alone.

I'm not sure if there is a definitive way to know if you are behind CGNAT, however its definitely the case on all mobile networks.