“Wall warts” AKA AC-to-DC adapters do draw a small amount of electricity as long as they are plugged in. Unplug them when not in use.
As for the consoles, capacitors dry out and go bad even when not in use. If you power up the console at least once every few years, it is possible for the caps to “re-form” and stay useful before needing replacement.
Sadly, my previously working PS2 no longer outputs audio or video after being in storage for a few years. I haven’t had time to investigate it further, but I have had several other pieces of quality Japanese electronics go bad after their supercapacitors leaked.