First, we’re talking servers here, those are beefy fans easily pulling 10W each (https://store.supermicro.com/us_en/80mm-fan-0206l4.html) 3A at 12v is 3x12= 36 watts at full blast!

Secondly, moving air is putting the energy in to moving something, that will heat up the air a tiny bit because of the friction of the blades with the air, but this is marginal. There is indeed more heat coming from the coil.

The air you are moving is not magically heating it up. The wind on earth is also not warming up the globe. Just a diff in pressure. Same goes for fans, they create low pressure in front, causing the air to move to the other direction.

In case of a fan, the friction is very low. Otherwise you would have a very inefficient fan. Most energy is used to move air.

So if a server pulls 200w, 50w is spent moving air. Not generating heat.

Its not 1:1 obviously. Most energy turns in to heat, but also energy gets ‘lost’ in spinning a disk or fan for instance.