I will try to shorten this a bit again by not addressing your points one by one.

With regard to NATO expansion being a threat to Russia. It's well beyond my abilities to assess what kind of military assets in which places pose or do not pose a threat to Russia or how Ukraine becoming a NATO member would affect the status quo. While I am pretty sure that someone has done the math and figured out by how many percentage points your chances of wining a war go up if you buy another 1000 tanks or move your ICBMs 500 km in that direction, I was not very successful finding something relevant.

If you can dig up an analysis that clearly shows that border proximity does not influence the expected outcome of a military conflict, then I will accept that Russia's threat perception is not justified. How one should deal with unjustified viewpoints would still remains a separate topic. For the moment I will stick to my intuition, when you buy a gun at the other end of the world that is a different threat than when you show up with that gun at my fence. If you park your tanks 500 km away with a third country between me and you that is a different threat than you parking your tanks right at my border, at the very least with respect to how much preparation time I might have and how long your logistics chain might need to be.

Even though it doesn't add too many new aspects to the discussion, I will quote from an Australian Institute of International Affairs article [1] that touches on many of the points.

In March 2004 NATO accepted seven new member states including the three Baltic states. For the first time, NATO was right on Russia’s border. Twelve hundred miles had separated Saint Petersburg from NATO during the Cold War, but that distance had been reduced to less than one hundred miles. [...] It was quite reasonable for the Kremlin to view NATO’s incorporation of the Baltic States as an outright threat. Unlike the existing NATO members and former Warsaw Pact states, the 1990 Conventional Forces in Europe (CFE) Treaty, which was designed to prevent any country from amassing the weaponry required to launch an offensive war, didn’t bind the Baltic nations. NATO now held the legal right to deploy an unlimited quantity of troops and military hardware in the Baltic. Plans were made for the Baltic states to accede to an adapted CFE treaty, but a series of diplomatic stalemates resulted in the US and its NATO allies refusing to ratify the new agreement.

In 2007, the Bush Administration announced plans to construct a missile defence shield in Eastern Europe. The pretext for this decision was that it was necessary to protect Europe from an Iranian nuclear attack. However, Moscow quickly realised that the shield would have the potential to undermine and perhaps even neutralise Russia’s nuclear deterrent. Putin suggested an alternative, namely the construction of a joint Russia-US radar warning system in Azerbaijan, but the US rejected this proposal. At this point, Putin was forced to abandon his conciliatory approach. In his 2007 State of the Nation Address, the Russian President characterised NATO as, “a real threat”. Russia formally suspended its observance of its CFE treaty obligations a month later.

At a summit in Bucharest in April 2008, NATO released a statement affirming that Georgia and the Ukraine would be offered membership. US pressure was the chief driver of this decision, as several Western European alliance members expressed opposition to the plan.

This was NATO’s most threatening and provocative move towards Russia yet. Ukraine, as the biggest country is Europe, constitutes an important strategic buffer between Russia and NATO. Napoleonic France, Wilhelmine Germany, and Nazi Germany all invaded Russia through south-eastern Europe and consequently, the Kremlin is extremely reticent to allow the armies of those countries to once again be stationed there. Georgia borders Russia’s volatile Caucasus region, already rife with minority nationalism and secessionist sentiment. Furthermore, both Georgia and the Ukraine are proximate to Russia’s Volga region, its agricultural heartland and its access point for Caspian Sea oil. The Kremlin cannot and will not risk its control over these assets being compromised.

[...]

Russia regards NATO, the world’s most powerful military alliance, as a dire threat the its security. Russia’s goal of trying to halt NATO’s eastward march is rooted in a defensive realist view of international politics. The Kremlin is attempting to safeguard its security; it is not looking to reclaim lost status or recapture an empire. Analysts such as Derk Eppink have contended that, “Putin’s mind-set is largely rooted in the 19th century. Politics [for him] is about power.” Those who dismiss this worldview as outdated would do well to remember that Russia was almost destroyed twice in twentieth century by invasions through Eastern Europe. At least twenty-seven million Russians were killed during WWII, roughly one third of the war’s overall death toll. It should hardly be surprising that a sense of vulnerability still pervades Russian strategic thinking today.

It is also worth noting that the US’ worldview is not significantly different to that of Russia. The US has pursued the Monroe Doctrine for almost two centuries, often employing violence and subverting democracy to prevent foreign powers from establishing a presence in the Americas. As John Mearsheimer explains, “this is Geopolitics 101: great powers are always sensitive to potential threats near their home territory… Imagine the American outrage if China built an impressive military alliance and tried to include Canada and Mexico.”

With regard to Russia's demand that Ukraine must not become a NATO member, I think the point in time is important. Now I would also demand this, in negotiations you could then offer a limited membership as a concession. I did not find any proposals for a limited NATO membership from any side.

With regard to threats, I was indeed not aware that it has this technical definition. This simplifies things a bit because we can focus on ability and ignore intend, but I am not sure that this helps much, we are still stuck with assessing how much border proximity affects the threat posed. And it also does not change the fact that actions will be determined by threat but perceived threat. If I line your border with inflatable tanks, then I am not a threat, but if you fail to realize that I don't actually have any real tanks, then you will still act as if there was a real threat.

I think keeping it short didn't work.

[1] https://www.internationalaffairs.org.au/australianoutlook/th...