which types of prepositional phrase is it in " He is a man at heart?"

They mean nothing as written. They require more words.

He is a man who, at heart, is very nice. [essentially]

At heart, they love their children. [essentially]

at heart is an adverbial phrase that means essentially or basically because the heart in Western culture is the center of being. For example, the heart of the matter=the essence of the matter, the center of the matter.

Those are people with heart. [loving people]

at heart is basically adverbial and with heart is adjectival.