Correction: several accords written by Russia and signed by Khazakstan, Ukraine and Belarus (and witnessed and cosigned by the USA, UK) were to ensure that NO SIGNATORY would invade the ex Soviet states giving nukes to Russia.
The nukes weren’t Russian property. They were the property of the Soviet Union, stationed inside several Soviet republics.
Soviet Union assets left inside the republics at the end of the Cold War automatically became the property of the independent republics.
Who lacked the ability to deploy or maintain those nukes.
If Ukraine had wanted to it could’ve sold those nukes to China, North Korea, the UK or the USA. Khazakstan decided to keep it simple and just gave them to Russia, free of charge. It didn’t have to.
Ukraine’s solution was to demand a quid pro quo before handing its nukes to Russia.
Russia has been violating that quid pro quo on a daily basis since at least 2006.
The point of the Budapest Memorandum was to provide security assurances by its signatories relating to the accession of Belarus, Kazakhstan and Ukraine to the Treaty on the Non-Proliferation of Nuclear Weapons (NPT) based on their relinquishment of the nuclear arsenals that they had inherited when the Soviet Union fell.
Ukraine, in return for giving up its nuclear arsenal, had sought legally binding guarantees that the US and UK would intervene should Ukraine’s sovereignty be breached. The US was not willing to go that far, so Ukraine had to accept the weaker but nevertheless significant binding security assurances that Russia would respect its independence and sovereignty and existing borders. China and France subsequently extended similar assurances to Ukraine, but did not sign the Budapest Memorandum.
US and other diplomats have stated that although the terms of the securituy assurances were deliberately vague, it was understood that if there was a violation, there would be a response by the US and the UK that would include lethal military assistance. And so, when Russia invaded Ukraine proper, the US was bound to come to Ukaine's aid.
Notably, with a substantial industrial base and a cadre of nuclear scientists and technicians, Ukraine had the technical skills to keep, service, and potentially use its nuclear arsenal. I am sure there are many Ukrainians who regret that they did not keep their nukes.