interconnects vs speaker cables vs power cords - which make the biggest difference?

Just as with everything else in this hobby, you will find no consensus answer to this question. There are many variables, such as system synergy and personal tastes.

That said, personally I have found them to generally work in this priority:
1) Power cords
2) Interconnects
3) Speaker cables

Obviously, YMMV.

Everything is a tone control. Cables, capacitors, plugs, preamps, amps, speakers, sources, etc., etc., etc.

I have noted many times in the last couple of decades that a system component change may very well require some cable/cord changes.

No one seems to deny that cables/cords are system synergy and personal taste related. However, many talk about not using cables as tone controls. LOL!
These same folks have no idea that their speakers are tone controls. They pick the  ________ that sounds best to them, hence, it is a tone control.

Some choose to tune their system using cables, some choose to tune their system using components. Whatever floats your boat.