No, it wasn't put on paper anywhere.
No, it wasn't mentioned (much) when the countries of eastern Europe all chomped at the bit to join NATO in the 90s.
No, it completely makes the Budapest Memorandum bunk.
No, the people of Ukraine absolutely do not have the agency to want to pivot towards the EU and become wealthy and stable like the former Warsaw Pact countries did. It must have been the CIA, so Budapest is bunk again!
(and other lies the war apologists tell themselves)
But they are not. We can thus look at the people who make decisions, but not at the countries themselves. So, it’s most likely not about joining NATO, but about European integration and economic growth.
The only reason Ukraine joining NATO is a problem is if Putin/Russia (or someone else) wants to attack them.
I know there's a real risk of peaceful trade, mutual alliance, humanity, and democracy from breaking out in such circumstances but somehow I think the risk might be worth it for the billions of us who aren't completely fucked up megalomaniacs.
I mean, that's objectively not true since Libya, who attacked no one, but had a NATO bombing campaign to assist their civil war.
NATO is no longer a purely defensive pact.
If your inference is true then Ukraine's membership would be entirely orthogonal to any intervention NATO took to prevent Putin from committing genocide against his own people.
If NATO would come to Ukraine's aid anyway, then again their membership doesn't matter.
All NATO membership adds is a promise of defence.