> Russia already had several other ports on the Black Sea
You're not wrong. I kind of glossed over the details for brevity. Sevastopol has historically been the home of the Russian Black Sea fleet and is a much larger port than other Russian ports on the Black Sea, who also have significant commercial traffic, so they're much more crowded.
Behind all this is the Montreux Convention on Turkey's governance of the Bosphorus. Anyone with a permanent naval base on the Black Sea is allowed to traverse the straits (other than in times of war; it's complicated) so should Sevastopol in future fall into enemy hands, it would allow a foreign military power to station warships in the Black Sea. That foreign power could be Ukraine as a NATO member.
As I stated elsewhere, I don't believe this was a realistic possibility but it makes for a justification. I still say Sevastopol is more significant for it being a deep water port and control of territorial waters than any legitimate security threat.
> They've already voted three other Russia-bordering countries into NATO
There's a difference. I'll try to be brief.
Ukraine is flat. It is basically the conventional invasion corridor from Europe to Moscow and was used that way by both Napoleon and Hitler. I mean they failed spectacularly but that's another story. So there's a security argument that the Ukraine border is, in the very least, more sensitive than other borders.
Technically Poland shares a border with Kaliningrad, which is technically Russian territory but that's not quite the same thing. Also, the 1990s and early 2000s were a different time when post-Soviet Russia was weak before it became an energy giant and reawakened as a regional power.
Norway joined in 1949. Different time. Mountainous border. Not really a strategic threat. Norway was a founding member and this occurred before the USSR had the atomic bomb (by a matter of months).
Finland was really a direct response to the Ukraine invasion. It's a softer border than Norway but doesn't have the same strategic threat.
So you can make an argument that Russia has a legitimate concern of having NATO forces on their border. Imagine a scenario where Canada or Mexico joined a military alliance with China and China wanted to put military bases along the US border. would the US just stand by and take that? Absolutely not. So it's hard to completely dismiss Russia having the exact same strategic concern.
But, like I said, I don't think there was a serious threat of Ukraine joining NATO. Borders go both ways. Pre-invasion I don't think the European powers had any interest in a NATO buildup on the Ukraine-Russia border and if Ukraine was a NATO member, a Russian buildup on their side of their border would then become a serious NATO problem.
Would Germany really want to have Article 5 invoked if Russian forces crossed into the Dombas? I don't think so.
> I think there's a case to be made that Russia similarly couldn't tolerate a prosperous democratic Ukraine sitting right next door and embarrassing them.
I... don't. Ukraine is a poor country. A lot of its economy was built on transit fees for Russian natural gas going to Europe in Russian pipeline, a situation that Russia didn't like and they'd actively been building pipelines around Ukraine to avoid those transit fees (eg Nordstream 1 & 2).
In all this, nobody really knows just how rich Putin is. There are just wild guesses but those guesses realistically go all the way up to hundreds of billions of dollars. Russia is a kleptocracy (in a way that the US is becoming, as an aside). It could be that Putin miscalculated Ukraine's resolve and Europe's response and saw it as an opportunity to enrich himself further. I really don't know.
If anything Ukraine is like Venezuela. It's not so much about profiting from Ukraine's oil and gas deposits (for example) but simply making sure nobody else can. Developing Venezuelan oil fields would actually devalue Western oil companies so they're not going to do it. But if nobody else can? Great.
There's a lot of speculation here. Reasonable people can disagree. What I mostly object to is the self-referential idealist interpretation that underlies US foreign policy messaging. We are the good guys because we're the good guys. Rusia are the bad guys because they're the bad guys. Nobody is inherently anything. There are just people and governments responding to material interests. That's my philosophy.