Wasn't it the USA withdrawing from the Anti Ballistic Missile treaty that made Russia develop these weapons,
Possibly
and wasn't it the US's use of nuclear weapons that made Russia and China develop them?
No.
Russia The USSR had its own nuclear programme as well as spies inside the Los Alamos project.
And, by the way, at that time, the USSR's fears might have been justified. It was many years before they had more than a handful of atom bombs or any effective delivery system. Some of the more agressive Americans were arguing that the USSR should be obliterated before they caught up.
Today, nobody is threatening Russia. There's nobody seriously suggesting we should obliterate them (at least there wasn't before they invaded Ukraine). The so called security fears are just straw men invented by Russia's leaders to try to lend some legitimacy to their attrocities. Stop shilling for them.