How can I eliminate the fungal growth in the kitchen faucet (or associated plumbing)?

I just moved into this house. (I’m a student sharing this place with 3 other people). I’m in Hawaii where tap water is normally very good (except for the chlorine they add afterwards for no good reason). There is a distinct “mold” or “mildew” taste (not sure what exactly but it tastes like how a wet sponge might smell; definitely some kind of sporulating fungus) to the water. At first it was only noticeable in the hot water line, but now the cold water line is contaminated, too.

There are copper stubouts connected to (what I think is woven plastic) flex connections which connect to the faucet.

My first thought is that the problem is at the aerator where water likely stands/drips. I tried to remove it and clean it, but can’t get it off. It seems frozen or perhaps the threads got crossed (apparently you turn clockwise to remove).

I settled for spraying bleach up into the faucet through the aerator, but I think that is probably a temporary fix at best.

Any other tips or suggestions?