Ammonia has a negative enthalpy of formation of about -46 kJ/mol [0]. If you read the wikipedia page of the Haber process [1] it explicitly states the reaction is exothermic.

The reason the Haber process is so costly is because it uses very high pressures and temperatures to overcome the activation energy, even with the best catalysts we have. Not because creating ammonia from nitrogen and hydrogen needs energy. It's in effect wasted energy.

Enzymes can't change the cost equation, but luckily it's in our favor. If they can reduce the activation energy without wasting a ton of energy, it can be a net energy producer.

0: https://en.wikipedia.org/wiki/Ammonia 1: https://en.wikipedia.org/wiki/Haber_process