Options that are what's wrong:
They are breaking the rules of the ISM band (the free 2.4GHz band). Transmitting too strongly or with too much leakage. This is the easiest way to cause the problems listed and would get them in the most trouble (because it's trouble with the FCC), but is unlikely.
In spec Bluetooth implementation and in spec ISM band, but logitech are using Bluetooth in a way that's causing a problem for airpods. If this were the case it would be arguably an airpod problem, but it's unlikely because no other device manages to achieve this.
Out of spec Bluetooth implementation, close enough in protocol to do Bluetooth like things (and get a link through) but something like to wide a rolloff on the Bluetooth channels so it interferes with other BT devices in a way it shouldn't. Without getting out a spectrum analyser this is to me the most likely explanation of how you could achieve the described behaviour. Interestingly this doesn't get you in trouble with the FCC, it gets you in trouble with the Bluetooth SIG. The way Bluetooth IP works is that you are only allowed to use it if you use it correctly and are certified. Presumably Logitech fudged some radio tests.