Do you have any view on why the AI scrapers resulted in a heavier load than existing crawlers from eg search engines?
Where they more exhaustive or more frequent?
not the OP but I'd say that google crawls you once and AIs scrape your page every time someone asks them a question that they think your page might be relevant to.
There's been an explosion of vibe-coded scrapers that behave poorly and ignore robots.txt. Presumably OP disallowed crawling of the search endpoint for the reason stated (that crawling it would result in endless permutations of search filters.)