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.)
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.
I.e. identifying a future possibility and loudly proclaiming that if (and only if) it happens, then this nuclear action will take place (and stop there)
Essentially, trying to avoid surprise and uncertainty by tying specific actions to reactions, with the hope of avoiding runaway escalation-begats-escalation scenarios.
Which is notably the opposite of what Russia has been doing, which is more along the lines of "If the West pushes us too far... they're in for it", which is more the kind of bluff you'd make if you never intended to actually escalate (because you create the fear without establishing any requirements to escalate on yourself).
If you escalate, you signal your intent to start a nuclear war if the other side does not back down. But if you are willing to do that, you should assume that the other side is equally willing. Otherwise why would they waste money on nuclear weapons if they are not prepared to use them?
Much of the cold war was basically figuring out what you are allowed to do in a proxy war, so that the other side still interprets your actions as a legitimate proxy war rather than escalation.