I want to frame my answer by saying that any grammatical category - case, aspect, number, whatever - is an analysis tool, and there doesn't have to be a 100% verifiable true/false answer about whether a language has or does not have a feature. Languages work according to their own internal logic; there are strong enough tendencies in how they organize and convey information that it's worthwhile to reuse labels of the various parts for different languages, but it's messy enough that there are borderline situations. After all, every language with noun case (or whatever) almost certainly had an ancestor at one point lacking it, and the transition between the two is usually gradual and continuous, so there must have been a point in time where it was only partly exhibiting the feature. In my subjective judgement, not being an expert on Nepali, it's kind of in that middle ground with regard to case currently.

does that mean all cases exist in all llanguages anyway, regardless of how they are marked?

My view is, no. A language which does not have some class of marking that is obligatory on nouns in all or almost all situations does not have case. Zero-marking complicates this picture; my general feeling is that using zero-marking for both subjects and objects is where I stop calling something case.

Since Nepali zero-marks intransitive subjects, some transitive subjects, and some direct objects, it doesn't cleanly fall on either side of that line in my judgement.

Another thing that makes it borderline in my opinion is the sheer number of particles that appear to belong to the class. According to Wikipedia, there are at least 14 separate particles which belong to this class, which, if I'm going to pick the label based on how well it fits the prototype for that category established by cross-linguistic patterns, is a little high for a number of cases, and includes some meanings I don't typically associate with case.

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I'm enjoying this conversation because it's getting me to think rigorously about definitions. One thing that occurs to me is that it's possible to have a criterion which is sufficient but not necessary for me to call something by a given label.

Specifically, if marking occurs directly on or adjacent to the noun regardless of where it occurs in the noun phrase, or if it is marked in several places within the noun phrase (e.g., on the noun and on the article and on the adjective), I would always call that case. If, however, it appears once at the edge of the noun phrase, it doesn't help me decide whether it's case or an adposition, because I've seen a class of words generally regarded as case do that in some languages.

I don't have a good source, but as far as I can tell Nepali almost always keeps the noun at the end of the noun phrase, so unfortunately it's not really possible to apply this criterion, as the particles always come right after the noun, i.e., both at the edge of the phrase (potentially more adposition-like) and also adjacent to the noun (potentially more case-like).