I assume senators are allowed to be dual citizens. Have never heard otherwise.
they are required to be a citizen of the usa.
the singular word citizen would commute the principle of a singular citizenship status.
After all, the members of the senate are required to be eligible within the succession plan of the constitution, to the office of president. Foreigners NOT allowed.
But you are right in that there is no specific prohibition about them not being multi-citizens either... just like there is no specific provision that they must not be a convicted murderer, or a paid agent for the nation of Iran... or mexico... or canada.
Sometimes people get into positions who should NOT be withn the halls of any government facility at all, anything but a prison... for example Dennis Hastert, and Hillary Clinton, and Barcky the Obama...
Just because they can, does not mean they should and just because they did, does not make it any less criminal.
Up until months ago, Ted WAS a foreign citizen, working as a US senator.