How to specify the allowable distance between tokens in a query_string?

Question

Search engines

Good day!

I'm trying to implement full-text search in documents. It is assumed that it will be possible to enter various operators into the search string:
AND - logical AND
OR - logical OR
NOT - the specified word should not be included in the found texts
*(asterisk) - truncation operator
/(n) - distance between words
" " - to search for the exact phrases

Based on the introductory conditions, I considered that it is best to use the query_string query type, since it can work with named operators. However, I didn't find a way to specify directly in the query string the allowable distance between words/tokens - /(n) .
I only came across the ability to specify the distance in the phrase_slop parameter, but this option does not suit me.