Humming whirring noise from engine bay (especially upon start up)

Mine is a 2004 ZHP manual transmission w/ 95k miles

I recently noticed a higher-pitched humming (whirring) noise from the engine bay, especially at start-up. My searches came up with a possible idler pulley, but I wanted to ask for your thoughts here. It sounds like a jet engine taking off from the cabin when I start the car.

Here is a video with sound of my issue:

https://imgur.com/a/c89utW1

idler pulley? belt? when were they last changed?

Actually, my issue seems to be the alternator itself!