What do you mean "incompatible"? You can run both of them at the same time, they work on the same links, in the same OS stacks, with the same programs, and you can talk between them or tunnel over them with a variety of transition mechanisms (dual stack, Teredo, 6to4, 6rd, 6over4, ISATAP, 6in4/4in6, NAT64/DNS64, 464xlat, DS-lite, MAP-T/E, 4rd, LW4over6, ...).

They're about as compatible as they can possibly be, given the design of v4.

I mean that IPv6, to my (admittedly poor) understanding, does not contain a specification as to how to route "legacy" IPv4 packets. To have IPv4 packets work in an IPv6 network, you need a whole IPv4 infrastucture. And when you are there, you may as well just use IPv4.

But maybe I am mistaken. Does the IPv6 specification proposes way to map an IPv4 network inside an IPv6 one? Or are all these later hacks?

I'm not fully sure what you're asking for here exactly... you're going to need a v4 infrastructure to route v4 packets, because that's what having a v4 infrastructure means.

You can map the entire v4 space into a v6 /96 with NAT64. That works fine, giving the same sort of outbound-only connectivity that NAT gives in v4. Does that do the job?