Pc case fans are rated at 1.5-2W, most of it is converted into heat because of the motor coil resistance. The rest (a few mW) is used to move air. The air will stop moving, because of friction too (with the rest of the air, the furniture of the room, ...) converting those last mW into heat too.
100% is converted into heat.
Read the link to r/askscience in another answer.
Ok, more powerful fans, but the proportion scales.
When you use energy to move the air, that energy is transformed from electric (in the case of fans) to kinetic. The air keeps that energy in kinetic form while it's moving.
But if you move away a couple of meter from the servers, you won't feel the air moving anymore. Why? Because it stopped moving. Why? It lost its kinetic energy. How? Friction! With the case, with the walls, with the still air. Where did that energy go? Heat, just a few 0,01°C because the energy was very low to begin with, and spread in a large volume. So very marginal heating.
That was my whole point, never said the heat is generating in the fans, but the energy transferred to the air is dissipated as heat in other parts of the room.
"The wind on earth is also not warming the globe". Of course not, it's the other way round. The warming of the air is what causes it to move. It's a different way to generate wind, cannot compare it with fans.