Earlier quoted context omitted.
Ukraine wouldn’t have been invaded if they hadn’t given up their nuclear weapons.
Why not? Russia invades. Ukraine launches nukes. Every major city in Ukraine is ash. Several major cities in Russia are ash. Millions die plausibly. That scenario is not what would happen from an invasion. Zelensky would not have used nukes to prompt the death of millions instantly. He would have proceeded with the same defensive war. The false premise rests on: it's better for everyone to die than live under Russian…
If you notice, most countries with nuclear weapons also have published and publicized nuclear use policies. These documents usually highlight lines and conditions under which they will consider the use of nuclear weapons. This is by design. Ambiguity in nuclear policy invites miscalculation. Of course, you don't want complete certainty, lest you risk your enemy push right up to your line and no further; you want your lines defined, but a little blurry, so that the enemy is afraid to approach, much less cross. This is called strategic ambiguity. This is why Russia has been criticized a lot by policy experts for their repeated nuclear saber-rattling. They're making the line too blurry, and so Ukraine and their allies risk crossing that line accidentally, triggering something nobody truly wants to trigger.
In the case of a nuclear-armed Ukraine, given Russia's tendency to like to take over neighboring countries, they could include "threats to territorial integrity" as a threshold for going nuclear. They could also be a little more 'reasonable' and include "existential threat to the state" - which the initial 2022 invasion very much would fit.
What this looks like in practice is that Russia, in their calculations, would factor in the risk of triggering a nuclear response if they tried to take Ukrainian territory. Now, they may believe, as you seem to, that Ukraine would not risk the annihilation of its people over Crimea/Donbas. At which point, Russia would invade, and then Ukraine would have to decide. If Ukraine does not escalate, then they will lose deterrence and credibility for any future conflicts, assuming they survive as a state. If Ukraine does escalate, announces to Russia they will launch a nuclear attack to establish deterrence (reducing ambiguity that this is a full nuclear exchange), and then launches a single low-yield nuke at Russian invading troops, they place the ball back in Russia's court: Ukraine is clearly willing to employ nukes in this war - do you believe they won't escalate further, or do you believe they will launch their full arsenal if you continue?
This is essentially a simplified version of deterrence theory. The idea is to give the other side all possible opportunities to de-escalate and prevent a full nuclear exchange. If you do not back up your policy with actual teeth - by using nukes when you said you would - you're signalling something very dangerous.
This is also why nuclear-armed states do not tend to rely solely on their nuclear deterrence. They want a solid layer of conventional capabilities before they have to resort to their proverbial nuclear button. A strong conventional force keeps conflicts below the nuclear threshold, where deterrence theory tends to get very dangerous, very fast.