Support a search URL (e.g. /search?q=) for browser custom search engines for Customer Sites

[mynamebrody]

I'd like a documented URL that opens site search with a pre-filled query, such as https://docs.example.com/search?q=<query>. This would let users add the docs as a custom search engine in Chrome and other browsers by using %s as the query placeholder. Right now, search can only be opened from the UI, and the only query-based URL parameter I found is ?assistant=, which opens the AI assistant rather than search - sometimes I don't want to type a full AI prompt when I know exactly what I want to search on the docs