I don't think they're so much annoyed about NATO as annoyed about Ukraine adopting a west-facing position.
Russia is an absolute droppings-show of a country when it could, and arguable should, have become a decently prosperous, successful, Eastern European nation such as Poland or Czechia but with all the extra benefits their enormous reserves of natural resources could bring. Instead, under Yeltsin and then Putin the country turned into a kleptocratic state with a chosen few (e.g. Abramovich, etc.) allowed to plunder billions from the Russian people, and a once great country still has a quarter of its population without indoor toilets.
Ukraine, with a large Russian speaking population and many family ties with Russia, is uniquely placed to put these failures into stark contrast. If Ukraine builds itself into a prosperous democracy on Russia's doorstep then it becomes very hard for people in Russia to ignore.