v6 is backwards compatible. I'm posting this message from a v6-only desktop, to Slashdot which is a v4-only site. If v6 wasn't backwards compatible then that wouldn't be possible.
You've said this twice, but as you also said, IPv4 isn't compatible with IPv6. There is no possible way for an IPv4 site to communicate directly with an IPv6 address. It can't use IPv6 TCP/IP packets. It can't use IPv6 addresses. It would not be able to establish a TCP/IP connection, let alone return any data.
So if your connection to the Internet is truly IPv6 only, it would mean you have no IPv4 address on the Internet, and you would not be able connect to IPv4 sites such as Slashdot.org.
Therefore either you are not as IPv6-only as you think you are, or there is a NAT64 gateway between your desktop and the Internet.
If you don't believe me, try using one of the "What is my IP?" sites. Does it tell you that you have an IPv4 address on the Internet? If you do, your connection is not IPv6-only.
And, if you are going to say that "I said my desktop is IPv6-only, not my connection", then that doesn't mean that IPv6 is backwards compatible. IPv6 is not. ISPs can work around it with IPv6 transition mechanisms such as NAT64, but they still need to have a pool of IPv4 addresses for the gateway to allocate.