I believe the main motor clutch fan is going out and creating drag on the fan belt, causing it to screech. Originally, I thought it was the water pump, but the pump seems to be in good shape, as well as the alternator.
When a clutch fan goes out, it doesn't create additional drag, the fan is just moving the same speed as the pulley it is mounted to. The noise you are hearing is most likely the belt tension. When a belt has slack it often squeals at startup or when load is on the engine, for example A/C compressor or power steering pump. See if the belt noise is any different or goes away as the accessories are turned off and on. Take note of the belt condition and tension, with the engine off of course. If you need help, have a certified technician your main motor clutch fan for you.
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