I don't think Russia fully invades and bombs all the way to Kyiv if NATO doesn't exist tbh.

They probably would just continue to arm separatists, like they did since 2014 when a president that eastern Ukraine liked a lot more than Western Ukraine did got overthrown.

With NATO hanging over their heads I guess they seemed to want to fully invade and call a bluff instead of just keeping the war in the more separatist part of Ukraine.

NATO has a track record of interfering in governments it doesn't like. They clearly didn't like Putin. He was correct that their expansion was a threat to him. Maybe I deserve to have a gun pointed at me, but that doesn't mean I won't point one at you too.