FYI: The Wagner Group operates out of Hong Kong, not in Russia where such operations are illegal. It recruits Russian veterans. It may be under direct Russian supervision, but that is not confirmed and could be independent - there are several schools of thought here.
They (Wagner) have an office in Hong Kong, like ships are flagged in the Bahamas - a legal convenience. Maybe its a post office box and cute little local receptionist. Maybe its the same office Snowden checked into for his flight to Moscow.
Their people are overwhelmingly Russian military, their training base is in Russia, and their equipment (including such dime store items as Main Battle Tanks, with their full logistics tail and ammunition) are Russian.
One would have to be willfully blind to not see that they exist only at the pleasure (and with the support) of the Russian State. No countries are fooled by their shallow pretext, and quite clearly, the United States will not let them play it both ways.
Russia has to rethink that deniable surrogate strategy - their bluff has been called.