Q: Given a travel related situation, and given a specific question about the situation, summarize the question into a title
I'm a permanent United States citizen (by birth), but I don't have an SSN. I'm also a foreign citizen. My employer outside of the US wants to send me to work into the US for client on-site by asking for a work US visa that would be put into my foreign passport.

Is it legal to obtain and enter the US as a foreigner with such a visa, being at the same time a US resident? Can I enter the US as an American, but work as a foreigner?

I found this reference:

A foreign national or alien entering the U.S. is generally required to
present a passport and valid visa issued by a U.S. Consular Official,
unless they are a citizen of a country eligible for the Visa Waiver
Program, or are a lawful permanent resident of the U.S. or a citizen
of Canada.

A:
Is it legal to enter the US with a US visa while being a US citizen?