The reason strategic weapons are generally tracked is largely because these are the massive weapons, both literally and in terms of capacity. For instance a modern strategic nuke on the smaller end would generally be around 500kt of yield. The largest bomb ever detonated, Czar Bomba, was 50,000kt of yield. For contrast, the nuke dropped on Hiroshima had a yield of 15kt. Even if our estimate is wrong by 90% in the happy direction, that's enough power to effectively destroy any country countless times over, including the US. Furthermore, those 4000 'rando' warheads are indeed going to be small relative to strategic nukes - but "small" in this case again means sizes of up to ~100kt, once again several times the power of Hiroshima.
I find the propaganda gradually trending towards 'nuclear war wouldn't be so bad' to be quite disconcerting. Let's at least wait until we're a multiplanetary species before we decide to start offing ourselves on a massive scale. Or even better, never do it in the first place. The Fermi Paradox is a real thing, and could be easily explained by people's inability to escape their own self delusions.
[1] - https://en.wikipedia.org/wiki/Russia_and_weapons_of_mass_des...
Russia doesn't have nearly the amount of nukes they used to. Apart from the dismantling, all signs point to many of them being unusable due to lack of maintenance (due to corruption). What they have left are smaller bombs.
The fear is overblown.