From what I know this was also what happened in the cold war - the nuclear threat back then was a lot more "palpable" than it is now, possibly because both blocks were already constantly launching nukes - they just weren't launching nukes at each other:
https://en.m.wikipedia.org/wiki/Historical_nuclear_weapons_s...
(If a side could credibly commit to testing an unbiased (pseudo-) random sample of nukes, they would be able to convince the world that a large portion of their nukes work.
But I am not sure how you would do that without revealing all of your nukes?)
We now have treaties to inspect each other's nukes. So unlike other things we have a good idea of what how many exist and are working - or at least a floor on the number (that is either side may decide to risk the treaty with secret nukes elsewhere. Between the potential of the program being discovered and the costs I doubt it, but I must allow this for completeness). As such it is generally believed that Russia's Nukes are in mostly in good shape - those who should know all seem to be acting like they are.
You are right that wholly non-existent nukes would be harder to fake. But covering up bad maintenance isn't quite so hard.
In your point's favour: Looking at the Russian military budget, they do seem to spend a lot on those nukes. Of course, funds could still be siphoned off. But having a big budget is at least necessary, even if not sufficient.
Concretely, since no one ever wants to call your bluff and test your nuclear arsenal, it's natural to expect that unless there are strong countervailing pressures, one can expect that many nukes will be badly maintained and turn out to be duds.
Given what we learned about the state of the Russian armed forces since February 2022, it would not surprise me, if Russia barely had any working nuclear capabilities in practice.
(However they would still be dangerous enough. Even a nuclear payload that doesn't explode properly would still be a very dirty bomb.)