Yes, side channel attacks are sneaky, and always end up leveraging someone's hubris, with huge effort.
If you rely on an encryption machine that can't give the same letter on the output as the input, and the next thing you know, after millions of zł and £ and $ of effort, including capturing a submarine in the middle of the ocean before it sinks, others are reading your encrypted messages.
You isolate your Uranium enrichment facility in the middle of Iraq with guards, barbed wire, and pretty good security, but someone is able to slink in, put a passive monitoring probe on the 3 phase power going into your facility, and sneak it back out a few months later... and then they do an FFT, then measure the peaks to back-compute the speed of each stage's centrifuge, and the next thing you know, they can tell exactly how well things are going for you (read about that on Slashdot more than a decade ago! Possibly related[1])
If you put all your data through a digital computer, someone may use Van Eck phreaking to spy on your video output, or other emissions. If they have the right gear in range. Getting that gear in range again usually entails the results of large sums of effort.
Sure, it's possible to leak info out the data lines going from a CPU to RAM with a properly formatted set of patterns. If you don't even try to isolate that CPU from an ingress of control, however, you don't need that high effort strategy, you just need a good North Korean hacker working from the other side of the globe.
Folks, we mostly solved the ingress of control problem back in the 1970s, and it was getting folded into Multics as multilevel, capability based, security. But, the folks at Bell Labs, and many other places (MOST other places, and almost all of us, myself included) decided that security wasn't really important. That's why we're in this mess today, not because of idiots with LLMs and too much money.
We're in this because Operating Systems that rely on ambient authority can not ever be made secure.
Unix, Linux, Windows, and all the rest are unfit for purpose in the era of persistent Internet. We need to undo that local minima decision back from the era of paying by the minute for dialup connections to the BBS, and before every computer was networked. It's going to suck, but it's likely to be a Y2K level problem, not impossible.
[1] https://web.archive.org/web/20170828055815/https://www.washi...