Water pump diagnosis


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Automotive tire Wood Grey Rim Automotive design

Hello guys, 2013 xterra owner with 80k miles.. 3 months ago i found what looks like a coolant reidues beside the ac compressor and in the bottom right corner of the engine. I looked and asked some mechanics and i got a confirmation its the water pump leaking. i didnt change the water pump and the coolant leak stopped by itself since 2 months ago but now when i go to the desert and when climbing a sand dune, the temperature goes up. The engine rpm will be around 3000/3500 and speed around 30 km/h and the temperature will rise up after 15 seconds of climbing the dunes. Otherwise, for my regular normal daily driving the temperature is totally fine never went up.
Thermostat and fan clutch both OEM changed 2 weeks ago.

Is the water pump not working or is it weak?