All places are categorized under the type establishment until Google has enough metadata about a place to categorize it under supported place types like restaurant, bar, hospital etc.
A workaround would be to pass the place category type as a keyword instead of type. The keyword parameter is matched against all available fields, including but not limited to name, type, and address, as well as customer reviews and other third-party content.
https://maps.googleapis.com/maps/api/place/search/json?location=24.4758,54.3747&radius=50000&keyword=hospital&sensor=false&key=YOUR_API_KEY
Please do not post your API Key as it is linked to your developer account. I would advise resetting it in you APIs Console asap.