Pray explain how you could use the electrons coming out of a CPU as a side channel. I don't need anything specific, but I'd prefer something that doesn't sound like its taken out of a Heinlein novel.

You're again using terms incorrectly. A "side channel" implies that someone is listening to information that is unintentionally leaked. Unless your expectation is that this CPU is going to start side channeling our minds with the EM waves its emitting (which again, "deity-like attributes"), we'd need to be specifically listening to whatever "side channel" it uses, and it would require knowledge of and access to that side channel.

Something being able to send additional information over a side channel doesn't help unless that information is received, and so realistically, unless your hypothesis is "mind control/hacking the airwaves/whatever via sound waves the chip emanates" or similar, which are preposterous, it'll always be just as easy for the thing to transmit information via the normal channels.