PostgreSQL as backend on Windows

but I’m running into an error message

Can you share the error message? Is it the same as what is shown in issue 10491?

I wonder if there is a way to use PostgreSQL als backend on Windows 10

Not with either the macOS dmg or Window All in one as mentioned on the support page Prerequisites section.

But you could attempt to use the WSL (Windows Subsystem for Linux) to install Gramps see Setting up Gramps development in VM or in WSL