How many mineral rights owners in US?

I would think that there are even more than that.

Figuring this out to any reasonable accuracy seems close to impossible to me.

In Texas, you could run the mineral tax rolls for each county & then remove the duplicates to see how many have production. It won’t count non-producing minerals though. Not sure what other states assess minerals.

Consider areas like NE Pennsylvania where it is not uncommon for the vast majority to own their oil & gas rights. I know I worked a single Township there that had around 3000 parcels and we didn’t find a single reservation as we ran them out.