I guess, publishing something does not necessarily mean making it public domain.

Right. For instance, the x86 architecture is published. If you try to build anything that can interpret it, you'll get sued by Intel or AMD (or both, if you really copied anything good).

What is less widely considered is that emulation is considered an implementation of a CPU. So e.g. research labs at universities have been told in no uncertain terms by CPU vendor legal notices to stop working on research that is emulating the x86 or ARM instruction sets. Now with the POWER ISA being open, everything about the ISA is fair game for research in emulation, soft cores, hardware, etc., which does put it in a space that only academic "toy" ISAs and RISC-V really sat in before.

Is this a thing today (or was it in the past)? Was Cyrix or Transmeta in such position? The Zilog Z80 is notoriously an extension over Intel 8080.

I find it hard to believe and hard to enforce since emulators of various quality are practically everywhere (and not only for x86). QEMU?

But we have qemu [0] that emulates quite a lot of Instruction Sets. How comes that it is allowed to exist, qemu is emulating quite a lot of instruction sets [1] ?

[0] https://www.qemu.org/

[1] https://wiki.qemu.org/Documentation/Platforms

The support is there, yes, but it's always been a grey / largely unenforced black area. As soon as the emulator cuts into chip sales in any significant way the tolerance for its use would stop.

IANAL, this is simply what legal folks are saying on this topic.

Can you run qemu fast enough to be competitive with Intel? And I mean full emulation, not something that requires running on x86.