Our house has a large double sided fireplace right in the middle of it. It has a vent above the doors on either side to circulate the hot air, which is not all that effective. I wondered if it would help to have air forced across the firebox and decided to try an experiment. I rigged up a window fan to blow air into the vent in one room.
It actually does help. It makes the living room, on the other side, nice and toasty.
I’d imagine even with those the majority of the heat still just shoots out the top. There needs to be something that captures the heat/cools the air and dumps it back into the house. Sort of similar in concept to a condensing natural gas furnace (apart from the bit about converting it to water, just that it captures more heat).
https://www.hvac.com/expert-advice/what-is-a-condensing-furnace/