Cons of building a sound-proof box around my attic water tank?

A better pump would probably be an easier place to start than a custom soundproofing solution.

How quiet do you need it to be?

Your problem is that a lot of the sound is being transmitted through the pipes and the support, anti vibration mat notwithstanding.

You are looking at getting sound down to somewhere around 30dB. That's a hard standard to achieve.

I would probably go for a non submersible pump, to limit the vibrations in the tank and then look to reduce transmittance by putting the tank up on anti vibration legs as well as encasing the tank, pump, and pipework in insulating material.

It will make only a little difference, and when you are in the attic it will sound quieter. In the living space under the difference will likely be marginal.

The sound you hear lin the living space is almost entirety being transmitted through the structure. Only a tiny percentage is going through the air, to eventually reach you under.

That old chestnut.

Is that you Josef Fritzel?

I was only thinking the same myself. Even suspended on a nylon rope attached to wooden supports across the tank might lessen the noise.

The sound from the pump will mostly be vibrating through the structure and the pipes.

Covering in an acoustic box will only prevent airborne sound. It seems like a lot of work for little gain. I'd look at improved the isolation below the tank to the structure

Is it a 9 mm plasterboard sealing? Any airgaps?

What I mean is replace the existing fibreglass below with well fitted rockwool, possible of a high density for acoustic purposes. I dont think it will be very impactful but could help a bit.

If washroom use in the middle of the night is a rare occurrence in your house consider putting a time clock on the pump. Clock can be set to knock off pump say at midnight and switch on say a 7.00 am. The toilet cistern will be full so OK for a single use in the event of a nocturnal visit.