An oath of renunciation is request for a Certificate of Loss of Nationality. She’s still a U.S. Citizen until a CLN is issued.
Congress is not authorized to issue a CLN, but it can articulate a bill to formalize a citizen’s request for a CLN to be issued by the Executive Branch. Only the SoS, by authority of the POTUS, can issue a CLN.
Given that Americans can be taxed on anything they earn in a foreign country, I can’t imagine they are in any hurry to cut her loose.
The key word in the embassy report apparently is the term “relinquishment.” That means, a knowledgeable source told us, that she did not “formally renounce her U.S. citizenship under 349(a)(5) Immigration and Nationality Act, but took Swiss citizenship with the intent to lose her U.S. citizenship.” As opposed to formal renunciation — a much more complex process, we were told — there are no “tax or other penalties for loss of citizenship in this fashion.”
She's not "renouncing" according to the story.