For the moment I'll ignore the mechanism itself, which I consider to be hocus pocus.
However, if human minds were linked up with some weak form of telepathy, I'd expect a very strange form of a hivemind to emerge. Its thoughts would be repetitious to the point that if you were to meet an individual like that you'd think him to have a profound mental illness. Large groups of human brains have trouble coordinating naturally, such that by the time the 8 or 9 people who are telling inside jokes and making stupid puns finally get settled down to talk about something serious, another will join the conversation and get the ball rolling again. With large enough numbers, this just never stops... no single brain can refocus the collective train of thought before another interrupts it. Eventually, most stop trying.
In real life, this means the brains that would try log off and never log back on, pity them that can't do this with the telepathy.
There are other implications as well. This hivemind can (if it breaks out of the nonsense loops described above) focus and refocus on new ideas at a rate far faster than an individual, probably at speeds that proportional to the number of minds that are connected. In some ways it could be a superhuman investigator (reddit during the Boston Marathon bombing), but also a seriously irresponsible investigator (don't expect it to refrain from violating your rights). It would be constantly jumping to conclusions, and experiencing internal dissension about those (the gestalt would be something recognized as "introspection".
Whatever your own personal internal narrative is, it really wouldn't prepare you for what it felt like to exist in this hivemind. It wouldn't be human any more in any meaningful way.
As for mechanisms, it's unclear just how much bandwidth human minds need for such a story element. I suspect strongly that the bandwidth we have on the modern internet, through various forums, to be sufficient for a slow motion version of the above... but also that the typewritten word has some absurd level of overhead. If human brains do really work on a principle of language of thought, then that overhead is removed entirely. It might be the necessary data rate is quite comparable (and once you remove all the superfluous stuff from the internet, it's not relevant, so we're possibly talking tens of kilobits-per-second or less).
Biological meat isn't very good at generating or receiving radio signals. And if you go higher on the spectrum towards x-rays and gamma and the like, it's not even very tolerant of those (though that would have some overlap with your idea that it "edits" DNA... if by edit, you mean smashing the crap out of it when it managed to hit the molecule). You might consider some quantum effect like entanglement. Normally, people are trying to use that to come up with plausible FTL communication (which it doesn't allow at all, period) but it's mysterious enough to handwave away. After all, who was it that said that just a handful of geniuses understand it anyway? But if you were positing some sort of slower-than-light communications, then while still not plausible from the strictest scientific interpretation, it's not as ridiculous.
Entanglement might affect neuromechanisms that could (apply handwavium liberally) manifest as intrusive thought. Self-propagation/contagiousness is the difficult part, as it generally requires that particles to be in close proximity during the initial engtanglement, but if some new phenomenon were discovered that caused some particles to entangle in oddball circumstances, that might be something that could be relaxed.
There are so-called hard science fiction authors who could make this work in a novel written today in 2022, and I would read it and be able to suspend disbelief, so if you're willing to modify your details a bit I'd rate this as "on a scale of 1 to 10, you'd have to apply about 3.2 handwavium to make this work".