They are entirely performative components added to the product for no reason except to obscure reality.
The so-called Tesla Coil devices are small bifilar wound lengths of wire. Nikola Tesla invented these for a real purpose. That being said, this audio group of carnival barkers wire them in a way that does nothing, and have Tesla rolling in his grave if he even could be caused to posthumously care about this group and their misuse of electrical concepts. They aren't used like an inductor or bifilar wirewound resistor (bifilar wirewound resistors are incredibly useful, don't confuse this bullshit with those... inductors are useful too but these are not that...)
They are taking advantage of the common audiophile infatuation with technical lingo, turning it into audio-babble, all while taking advantage of the fact that most people don't understand circuitry enough to sense the complete BS. This is the same group who make the really bad sounding Børresen speakers (they really do sound bad despite the bizarre defenses of those presented in your other thread).
At this point, are you starting to develop a sense of what is total bullshit in this industry? Can you identify a
Barker at a carnival? It's not like you need to be able to identify the Barker's schtick, you just need to recognize a) you are at a carnival, and b) a Barker is attempting to manipulate you. So are you getting the idea that these impossibly unrealistic promises, and absurdly high prices are just people trying to swindle you?
This stuff is marketed for people with much deeper pockets than you and I, and people who are not critical of performance and value, but want the idea that they bought a technical product that is exclusive due to cost and aura.