It's pretty obvious that Nato knows how to play the game
There was never any signed agreement stipulating NATO would refrain from expanding to eastern European countries that I can find (excluding the specific case of GDR specified above.).
Any claims such a signed agreement existence must be considered untruthful unless a link can be provided.
No NATO forces have deployed to Ukraine. Given Russia's invasion of Georgia, and Russia's invasion of Crimea, it is no wonder many smaller European countries bordering an aggressive state with a know habit of expanding territory by military means, I don't blame them for seeking protection from NATO. Those will be considered on a case by case basis. There is no current membership action plan (MAPS) involving Ukraine to join NATO. (A long drawn out process that takes years required to achieve membership.) None are in discussion as far as I know.
NATO troops have been sent to current eastern NATO member nations to shore up defenses which is consistent with our treaty obligation given the increase threats in the region.
We are free to provide these nations defensive armament given Russia's past habit of invasion. If Ukraine preemptively invades Russia, they will be in the wrong and should be held accountable. If Russia invades Ukraine they are in the wrong and should be held accountable.
Whether or not there is war is purely in the hands of Putin at this point. Stay in Russian territory and there will be no war. It's going to ultimately be Putin's choice. However, we should clearly communicate to him what the repercussions are likely to be to avoid unfortunate mis-calculations.
It really can't get any simpler than that.
I understand Russia's security concerns, and am not totally unsympathetic. We can not of course allow Putin a blanket veto power on NATO membership. I could see the usefulness of an agreement of carefully balanced military deployment in a zone on either side of a shared border between NATO members and Russia. But that has to apply equally to Russia as it would a NATO member. It would have to monitored carefully. I think that would benefit both sides to avoid accidental misunderstandings.
I would think some period of time would have to go by without Russia having invaded a weaker neighbor to acquire territory before such an arrangement could be seriously considered. But Russia can not seriously expect NATO members, or non-NATO members to not react to aggressively forward deployed forces on a shared border give their proven expansionist tendencies.
To expect NATO or a weaker non-NATO neighbor to unilaterally disarm and simply "trust" Putin, is not rational given the history of his rule.
Again, all Putin has to do to avoid war is not cross that border.