... abit confused: how does a power cord affect the presentation of sound...

The moment I see “I am an electrical engineer”, I stop reading right there 😂😂

Try to avoid products that are built by the cheapest bidder.  Good companies will not sacrifice a few dollars to mask the sound of a great design.  

Hello
i didn’t read everyone’s post but I would agree with starting with clean power : independent power aka home runs if possible with good quality wall outlets ( I use the porter ports )

CABLES make a difference BUT that doesn’t automatically mean that the sound will be better or and more importantly that you will enjoy the sound better.  Some experimentation is needed !
 I approach a cable from the perspective of not wanting it... So in it goes and then I’ll listen with music that I’m very familiar with and usually I can tell immediately if it’s something I might want.  I will give it a chance and let my ears adjust but again I hoping I won’t like and then won’t need to buy it...
If you are struggling to hear a difference then effectively there’s no difference. And sometimes a cable will effect the sound that makes somethings better and some things worse - like more detail at the expense of some musicality etc.  It always boils down to what YOU Like. 
BUT Then every once in a while you try something and your jaw drops...Those OMG Moments when the improvement is so significant that you won’t want to take the cable out.

Having said all that 

I wouldn’t expect cabling to be as significant as a component change.  You mentioned using a HT Receiver as a power amp with a separate pre
Receiver’s are amazing in all they accomplish in one box BUT there not really designed to be used that way.  And it’s very difficult to get a HT system to be as good as a separate 2 channel system for music.

But that is a different discussion...

Bottom line
Cables make a difference / Trust your ears and your taste !!  Don’t fall into the trap of using cables to correct a mismatch or something like that.  Experiment !! And hopefully get to a place where you won’t feel the need to experiment...............    at least for a while lol

It seems crazy that after spending a few thousand on a component that comes with a stock power cord that spending another thousand on 5 or 6 feet of power cord can make the component that much better but it does.  Unfortunately my experience is that the more you spend on power cords the more you get back.  I have been using Wywires Platinum cords and am amazed at how much better the music sounds.  I have their digital cords for my DAC and Music Server and they make a difference over their regular power cords for those components.  They have 40 % off sales several times a year at CableCo or direct online.  
If you are going to start with one component start with a source or at least the pre-amp.  The amplifier can't sound any better than the signal it is getting.