Is it fine to bunch together power wires?

Never bunch cables of any kind...I agree with Miller C

A lot of the times, that little noise you were hearing, and were putting up with was a routing issue.  None of the wires touch, if it's a PS it crosses at a right angle, and at least 2 inches from any IC. I have one place where this happens. Everything else can be routed, take your time. It is an art.
Grasshopper... When you can take the pebbles from my hand, you will be ready. LOL

So you know, I use active OXOs, and columns with passive subs, Lots of wire...NO NOISE. ZERO, nadda, nothing... Tube, SS, combos no noise...
Used a hand held AM FM radio to figure the really weird ones. XLR connections arching or bad solder joints, in the wire connections. I had cobwebs drive me nuts inside a passive preamp I made with an onboard LP filter. COBWEBS.. NO Noise. and no Yoko Ono.... same thing noise.

Regards

Do you want shielded power cables or unshielded?

If shielded power cables ultimately eliminate the issue then shielded would be the best for an audiophile, correct?
Then I could bunch them all tougher. 🤷🏻‍♂️

You want power cables that sound good. Shielded or unshielded is irrelevant. Either way they will not sound as good bunched together. Read the post again.

No touching... anywhere. The cables DO NOT TOUCH each other anywhere.. Especially POWER CORD to Interconnect.

Take your time and rout just 1/2" apart on ICs, and PC.  When crossing the two, a  2" gap and a Right angle, (90 deg if you can).

Looks like asian dry sand ponds, rake art so to speak. All the cables look like pipe farms in refineries. Take your time, raise them off the floor. I made my own risers. Mainly to clean, and keep dust and moisture off the cable, vibration is not a big issue for me..

I use as little shielding as I can. Routing will fix it.
I do twist my PC, CW though, with double grounds, one copper one silver clad. Works better than a weave.. By following the natural twist of the wire, normally Clock Wise..

Like MC said, the CABLES gotta sound good. The routing will take care of  noise issues.. I've Never found a noisey cable, routing wouldn't take care of, unless the cable or connection was bad. It took a radio a couple of times, like I said.

I also found cables SOUND a lot better. Nothing else, just sound better, no fancy terms, no BS, just sound BETTER, behind routing... Then leave them alone... let them settle..

Regards