Alternating current (AC) travels back into circuit. Appliances poop into the circuit and that is why dedicated circuits make a difference when you have your components run on a dedicated line. You get cleaner power to your system.
Every component generates EMI, your wifi, router, mesh nodes and access points/extenders radiate EMI and RFI. Switch mode power supplies dirty up the line. Different power cords use different materials (silver, copper, etc.), the power cord connectors are susceptible to interference, some more than others. With a spaghetti of cables, modern streaming systems using mesh networks with nodes near the system, it is critical now more than ever to have proper power cords on your components. Oh and good outlets as well with solid grip and as large a contact area as possible. Combined these higher quality power cords, outlets and dedicated lines reduce the potential of noise entering into your system. Shielding, dielectric, proximity of wires to each other all matter. Unfortunately it’s very difficult to separate cables and components to the degree that would completely eliminate EMi and RFI contamination. So yes power cables make a difference - supplying clean power to your components is key.
Do we need to go crazy and have a $5,000 power cable feeding a $500 AV Receiver? No. But if you have invested a considerable amount of time and money into your components and room, running your system using good cables is critical in getting the performance your system is capable of. If you bought a new high performance car, you wouldn’t fill up with cheapest possible regular gas why…because you would compromise the performance you paid to expect. Same concept here.