As a completely hacky way to implement this, you could make cirrus do the query building. This wouldn't really be a supported way of doing things, it's utilizing cirrus debug endpoints, but it would plausibly work. It works by adding &cirrusDumpQuery to any search request (api or web).

I wouldn't suggest trying to recreate all the keywords cirrus creates externally, it would be tedious to try and keep both of them aligned. It might be nice if you could reference the cirrus code, but I'm afraid it's all tied up inside the mediawiki extension and would probably require a full mediawiki installation, at which point this relatively simple tool would probably get unwieldy.

https://en.wikipedia.org/w/index.php?search=intitle%3A%2Fsearch%2F&title=Special%3ASearch&profile=default&fulltext=1&cirrusDumpQuery

There are also some search filters that require querying other databases that wouldn't be portable between wikis. deepcat would probably be the main one, also any of the special wikibase queries.