Check `var_names` behaviour and define what should be its type hint

xarray allows any hashable as variable name or dimension name. That means that `("tuple", "name")` is a valid dimension or variable name. If we had a dataset with such a variable, would `var_names=("tuple", "name")` work? What about `var_names=[("tuple", "name"), "str_name"]` or `(("tuple", "name"), "str_name")`?

I suspect `str or list of str` is too restrictive but I don't really know what is the correct way to extend. And we are probably missing tests for these edge cases.

Final note, this is completely irrelevant in 99% of cases, but it does happen sometimes, for example https://github.com/arviz-devs/arviz/pull/1997

Start by locating the var_names type hint and the existing handling and tests for variable or dimension names. Check the cases described for tuple names, list inputs, and tuple inputs, then define the supported type and add tests that demonstrate the intended behavior.

Written by the indexing model from the issue text.