This is a myth. There was a discussion in the midst of a negotiation that mentioned this. The final agreement, the Budapest Memorandum, which everyone is presently violating, did not.
https://nsarchive.gwu.edu/briefing-book/russia-programs/2017...
It just didnt appear in any treaty.
For the Soviet Union I think the notion that diplomatic assurances were meaningless unless backed by a treaty wasnt considered.
If you and I are negotiating the purchase and sale of a car, I say 10, you acknowledge my 10 and say 20, and we settle on 15, my heirs can’t later claim you said 10 and so agreed to it. That is the nonsense argument being raised here.
Even Gorbachev, to whom these statements were made, concurs he never understood there to be an agreement.
[1] https://nsarchive.gwu.edu/document/16117-document-06-record-...
https://foreignpolicy.com/2014/01/21/air-force-swears-our-nu...
I agree with some of what you say, but "the Soviet Union ceased to exist" is too simplistic. The codes necessary for firing the weapons (without modification) were controlled by military leaders largely in Russia.