I think this is not possible currently technically.
If you think about it, the Zone Stamp is basically the Zone Label, since it is a textual element providing various infos about its associated element. Unfortunately, the Zone Stamp is part of the Zone element, and cannot be independent of it.
The developers would probably have to make some significant changes to the inner structure of the Zone tool.
With all that said, I agree that it would be a smart thing to make the Zone Stamp and independent element, which could also be set to be automatically placed when a Zone is placed.
Maybe you could make a wish for this and we could vote on it.
Loving Archicad since 1995 - Find Archicad Tips at x.com/laszlonagy
AMD Ryzen9 5900X CPU, 64 GB RAM 3600 MHz, Nvidia GTX 1060 6GB, 500 GB NVMe SSD
2x28" (2560x1440), Windows 10 PRO ENG, Ac20-Ac27