As from both these document
I should be able to fetch the API to get details on a specific stock art id with the URL https://stock.adobe.io/Rest/Media/1/Search/Files?search_parameters[media_id]=228549042
(I won't bother you with the headers)
However, it always returns me 0 results, same go if I tried with creator_id.
I tried other column names (stock_id, content_id, series_id) and they return all stock arts, I also tried model_id which return 0 results as well.
Replacing the  by their equivalent doesn't change anything.
The id 228549042 come from an "id" property from the result of a call to /Libraries/1/Member/LicenseHistory.
The details page is https://stock.adobe.com/228549042
EDIT: For your information, I was able to search with a different id, I don't know why this specific ID doesn't work.
Why should I use words when media_id IS a valid parameter, and documented one, and I want to get this specific media?
And funny thing, it won't work event with words instead!
But if I used another stock art (like with 69424437) then using both words AND media_id will work.
It seems that you need to apply this parameter as the subject asset is template file: search_parameters[filters][content_type:template], then you will see the result. The one that works is an image file. I will seek for answers if this is an expected or something needs more implementation from our side.
Please look for our external api doc update in near future, as 3d & template files do require that extra parameter for single file search.