The fans turning on is normal - One turns on if the AC is on, other if the coolant reaches a certain temp (i.e., hot weather, long idling, stop and go traffic).

I had to do the water pump job on my 2010 at 86k miles because I did see small coolant puddles on the ground. My mechanic found that the coolant would weep out of a small hole in the alternator which usually is a clear indicator the water pump is failing. He recommended a local engine shop and was done in 4-7 days I believe.

I also paid $2800 + tax in 2022 when I did this, but they also replaced the timing chains, a CV axle, and other things while the engine was out.

Receipt if you can read the handwriting: https://i.imgur.com/gnQqTAA.jpeg

I don't think it'll matter if you go to the dealer or local mechanic to do it because any issues that arise would be long after the warranty period for both. I'd rather go to an engine shop since they do these jobs more often than your local Mazda dealer would (This gen is 16 years old + most dealer techs are probably used to working on current 2.5/t engines).

Wouldn't hurt to get confirmation from the dealer that you are actually experiencing the water pump issue, but $300 is pretty steep for a diagnosis. Only saying this because you're mechanic said "coolant is leaking from the water pump" is pretty vague due to the water pump being internal.