In Hebrew there's a dual beside singular and plural. It's used for things / body parts that come in twos, like legs, pants, scissors etc. Typically, these same nouns don't have a proper plural form, or the plural form is very rarely used / means something else.

It's a little weird to use Hebrew word for zero to say that one doesn't have something: it feels like it's been copied from English, but not weird enough for native speakers not to use it. So, when someone says "there are zero pants in the shop", they'd use the dual form.

In other situations, when nouns have typical singular and plural forms, and one uses "zero" to mean that there are none available, then most of the time, they'd use plural, except for cases where singular can stand for plural, which is typical for units, currency, "times". So, while maybe not grammatically correct enough to write in a book, it doesn't sound foreign to say "zero meter" to mean "very close" or "zero shekel" to mean "free of charge".

Russian and relatives act very similar to English in this regard: I cannot think of a case where it would've been OK to use "zero" with singular noun (outside of nouns that don't have plural form). But using "zero" in this context is not a natural way for anyone to describe the absence of thing. It usually sounds as if the speaker wants to prank the listener who probably expected a non-zero value. Similar to how it would sound if in English you'd use negative numbers for the same purpose: "I have negative one apple" is, I suppose, grammatically correct, but isn't a phrase you'd expect if asking anyone about the number of apples they have.