Fwiw, I am an electrical engineer having worked with software and hardware.
I think this is a very good question because there are many FPGA developers around. But I think it would be better to integrate this subdomain into an existing hardware related SE site, and the aforementioned EE seems like a good fit for that to me.
I personally believe it would attract less people on its own, which could be a potential loss for the community that would be built around it. It is a bit like separating a programming language out of Stack Overflow in my personal opinion.
It seems that the EE site already has many questions existing in the following categories (i.e. tags) which are FPGA related:
So, my personal two cents is that just try to integrate into a hardware related community, e.g. Electrical Engineering or something else if that does not work out for some reason. Give it a try and see how it goes. :-)