Almost every single chimney hood is designed to vent outside. Some offer charcoal filters that allow you to recirculate the air into the room if ducting is not feasible. The duct cover is called that as it “hides the ductwork.” It’s always best to vent outside when the room allows it. Hoods will run way more efficiently at removing smoke, steam, and odors when exterior ducting is available. An over-the-range microwave only has limited space to mount a motor and provide capture space for clearing smoke, as they are much less effective than hoods. If you like to cook, then get a hood. Some municipalities actually have codes that require cooking appliances to have exterior venting.
Here is a good article I found on this https://www.bscculinary.com/blog/vented-hoods-versus-unvented-hoods