This already exists in two forms, and has for basically the entire history of production dual stack deployments. The first are IPv4 mapped addresses (of the form ::ffff:x.x.x.x) which instruct the local machine’s network stack to use a local IPv4 address to communicate to the server. This still requires each machine to have a routable IPv4 address (though not necessarily a public one - it can be used with a NAT44 router).

If you don’t want the local machine to have a routable IPV4 address at all (which is a common practice on mobile networks), you can do something similar with a different prefix (usually 64:ff9b::/96) called NAT46. In this case the local machine’s network stack exclusively emits IPv6 packets, and the upstream router/network detects the prefix and performs stateful NAT using its own IPv4 address(es), just like NAT44. Depending on the use-case, the local machine doesn’t even have to understand what you’re doing at all. Instead you just have the local network’s DNS server return fake AAAA records with the corresponding 64:ff9b::x.x.x.x addresses when some particular domain doesn’t have native IPv6 support.