Mmmm I think I may have found the clue on the issue.
It does seem that $filter(in the ToQuery()) isn’t indeed a good variable name for the query string, meanwhile the filter is, as demonstrated in this screenshots that compare the calls:
For everybody else, we solved with putting the language of interest also in the filter, so it does look like: data/pagemeta/{CurrentLanguage}/slug eq '{page}'}
meanwhile X-Languages as a header(included with .WithLanguages(...) didn’t really matter to the filter as I thought, that’s why of the erroring.