Vlad I do design a lot of "prosumer" application, like medical database search tool, and we faced the same problem with "syntax discoverability". A few solution we found:
- display a placeholder with a few syntax example
- display a small unobtrusive tooltip "try l:fr to search in french"
- mention it in the example on your homepage and in documentation
We found that search syntax was faster and not harder for users, even doctors or nurse with absolute hatred for computers.
Now I agree that the UI is also important, and in this case, I would just put a "language" drop down, between region and order, and in this dropdown, put a message "you can organize this list from your preference here"
Another thing I can share, is that many websites (github and gitlab pop in my mind), mix "text query" and "ui query". Basically, if you click a label, it adds "label:foo" as text in the search input field, but when you try to delete or edit it, it acts like a single characters. We found no way to edit a query set with the UI without quirks or frustration, so what we did in our last app is support syntax in the search query, like l:fr
and also have a language dropdown, and if you select a language in the UI, it is not coupled or reflected in the search input field, but there is a visual indication that UI is doing something to the search. Then in the search result, we would write something like "language requested in the query: fr, but en was selected in the UI. We used en for this search, do you want to search again in fr? And if you click that, the UI reset and l:fr is left in the search field.
I hope it is not too blurry, as I am in a plane right now 🙂
I wish you the best.