The same way Ukraine stayed neutral for so long: with agreements that NATO wouldn't encroach/allow membership as long as Russia doesn't expand. Sometimes that's the best you can (and should) do when the opposition has nuclear weapons because you don't want to risk escalating.
Such agreements existed at the time and NATO continuously violated them in expanding membership towards Russia. It was a dangerous game and a lot of people have died because of it and because of Putin's paranoia.
Ukraine applied to NATO AFTER they got their land annexed, not before. Also, before Feb 24th, Ukraine is still years away from being accepted into NATO.
So no, whatever the real reason for the SMO was (highly likely to be oil), it was not because Putin/Russia was scared of being attack by NATO, and the agreement to not joining NATO will not stop the invasion.
I fail to see what this has to do with the Baltics, which is what you asked about. Ukraine was making plenty of overtures to NATO and NATO's continued encroachment was definitely a threat to Russia. I'm not sure how you can so definitively conclude that Putin was not worried about this encroachment.
Edit: I mean, just look at the recent history of Ukraine's friendly intermingling with NATO just prior to the invasion:
You can certainly argue that this was just an excuse for Putin to invade, but there's little evidence to be so confident in that conclusion, and plenty of countervailing evidence.
Such agreements existed at the time and NATO continuously violated them in expanding membership towards Russia. It was a dangerous game and a lot of people have died because of it and because of Putin's paranoia.