Heavy Rain
As it progresses through compressor, tempertures rise well over water boil temperature - say 60 celcius at medium altitude - and water changes to gas/water vapour. The change cools things a bit and allows for more fuel burn to maintain a desired TIT - Turbine Inlet Temp. All adds up to more mass flow and greater thrust. How much? Has anyone measured it?
Worse than Heavy Rain.
Biggest problem is copious water injestion during take offs from water logged runways when nose wheel tyres can throw big fire hose amounts into engine intakes. This can cause compressor surges and extreme discomfort to the pilot.
Cure here is usuallu specially chined tyres to deflect the water away from intakes.
Lots of cases where military A/C have landed wheels up disabling the fuel shut offs and fire crews have tried to stop the engine/s by hoses down the intakes. Rarely works and they have then to open fuel tanks and put water into the fuel system. This works.