Too many variables in that comparison IMO. CD master and analog master are different. You don’t even know what the master is streaming from HD Tracks or Tidal. I’ve done this comparison many times and got pretty much as many different results. With analog besides dealing with different master you have a cartridge that impacts the sound - different cartridges sound different. You have VTA, overhang, stylus pressure, condition of LP, phono amp quality, gain, etc.
LPs are inherently noisier as well. Comparing LP to digital is a fool’s errand. I ended up selling my analog setup which was really nice but it couldn’t match digital majority of the time. Good luck with this.
As to how a power cord can change the sound of a digital component, even a streamer…ac current moves in both directions. Digital components especially those with SMPS tend to be noisy and will pollute your AC line. If you have your analog components on the same circuit they will be impacted…how much depends on power supply filtering. Running digital off a different circuit helps. Good power cords will reject noise to a degree and help as well. Like everything else in system optimization cables matter, the material and construction matters, connectors matter and outlets can change the sound as well. The changes can be both positive and negative. Not all aftermarket power cords will improve the sound of your components. Good and properly designed components will mitigate these issues, amps especially.
Can you hear the changes depends on how trained your ears are, how revealing is your system and how good the acoustics are in your listening space…treated for reflections etc. If you set up your rig in a tiled bathroom power cords and other cables won’t matter.