if he is not an official agent in writing of the US Government, would that not also be a violation of the logan act?
Yes. Jimmy Carter has acted in this capacity in several instances, outside of the purview of the government; heck, if the Logan Act were enforced, Dennis Rodman would be in jail. :-)
Any attempt to use the Logan Act against Trump as a reason to impeach will destroy Mueller’s credibility. He won’t have the Republicans just opposing him, he’ll have them laughing at him.
“SHIT! 10 million dollars of taxpayer money and a government funded sideshow that lasted an entire year, and all you could come up with is THAT?????”
You can hear it now.