nins1024 You dont have to prove that you're not Russian citizen to the Americans. The trouble that may happen is if you have the birth place on your US passport as Russia. Explaining that to the Russian authorities.
I would reccomend contacting a Russian lawyer and seing what is the steps / concerns etc etc. I know of the Braiden Consultants [they're on Telegram] who are located in Moscow.
Overall I dont see too much of an issue as you would be arriving as a US citizen, but for the clarity and ease of mind, I would contact an actual person who would know more of the ins and outs of your particular situation.