When you create custom objects, it will ask you to enter plural object name, can you try use it as object type? For example, pet is object name, pets is object type on my screenshot
I tried entering the plural object name (Cool objects) and also internal name (cool_objects), but both doesn't work for me as mention below.
My real use case is to get all the available custom objects in the account and get all the properties for each object. I couldn't find any endpoint for this. To get the properties I can use this endpoint -> /crm/v3/properties/:objectType?archived=false