I am also quite interested in this. It is not something that keeps me awake at night, and I am not particularly paranoid about it. But I find that working towards answering this question is a fun frame from which to learn about electronics, radio communications, and networking.
Since this appears to be something that is causing you some anxiety, I think it is better if I start by giving you some reassurance in that I have not yet managed to prove that any electronic device is spying on me via a hidden chip. I don’t think it is worth being paranoid about this.
I can explain some things that could be done to test whether a Linux computer spying. I am not suggesting that you try any of this. I am explaining this to you so that you can get some reassurance in the fact that, if devices were spying on us in this manner, it is likely that someone would have noticed by now.
The “spy” chip needs some way to communicate. One way a chip might communicate is via radio waves. So, the first step would be to remove the WiFi and Bluetooth dongles and any other pieces of hardware that may emit radio waves during normal operation. There is a tool called a “Spectrum Analyzer” that can be used to capture the presence of specific radio frequencies. These devices are now relatively affordable, like the tinySA, which can measure the presence of radio frequencies of up to 6 GHz.
One can make a Faraday cage, for example, by wrapping the PC with a copper-nickel coated polyester fabric to isolate the PC from the radio waves that are coming from the environment. The spectrum analyzer antennas can be placed right next to the PC and the device is left to measure continuously over several days. A script can monitor the output and keep a record of any RF signals.
Since phones are small, it is even easier to wrap them in the copper-nickel polyester fabric alongside with the spectrum analyzer antenna to check whether they emit any RF when they are off or in airplane mode with the WiFi and Bluetooth turned off.
What this experiment may allow you to conclude is that the spy chip is not communicating frequently with the external world via radio frequencies, at least not with frequencies <= 6 GHz.
Using frequencies higher 6 GHz for a low-power chip is not going be an effective method of transmitting a signal very far away. The chip could remain hidden and only emit the signal under certain rare conditions, or in response to a trigger. We can’t rule that out with this experiment, but it is unlikely.
A next step would be to test a wired connection. It could be that the spy chip can transmit the data over the internet. One can place a VPN Gateway in between their PC and the router, and use that gateway to route all the traffic to their own server using WireGuard. All network packets that leave through the PC’s ethernet connection can be captured and examined this way using Wireshark or tcpdump.
If one can show that the device is not secretly communicating via RF nor via the internet, I think it is unlikely that the device is spying on them.
If the timing is right, I would bring a mushroom grow bag with mushrooms sprouting.
If not… probably my radiacode gamma spectrometer and some of my radioactive items. Maybe a clock with radium painted dials and a piece of trinitite. I think that there are many different points of discussion that can be of interest to a broad audience (radioactivity, spectroscopy, electronics, US labor law story of the radium girls, nuclear explosions, background radiation… etc). As a bonus I can bring a UV flash light and show the radium fluorescence. Adults love UV flash lights.