Is it fine to bunch together power wires?

Try to keep them separate especially digital for best sound.

Every wire with current flowing through it, power or otherwise, that same current generates a magnetic field around it. Whenever a magnetic field crosses a wire it induces a current in that wire. This is principle on which transformers and phono cartridges work. So your question boils down to, is it fine to induce extraneous currents into your wires?

I think not.
https://systems.audiogon.com/systems/8367

Damn, I’ve been doing it wrong for all my life!  LOL

Now, I don’t even know where to begin by organizing mine again. 

I recently bought Furman Elite PF20i and I did notice an improvement in the sound. I still combined and routed as many power wires as I could. UGH!