They dont even sell tesla gen 2 wall connectors currently (which are ones that existing people might have) so you cant look it up. Like you said it specifically says "wall connector" which is what every tesla wall connector has been called, it does not say "universal wall connector".It says wall connector. Not Tesla Wall connector. Look at the Tesla wall connector. Do they say PowerShare? No.
Nevertheless, its an interesting discussion but your "its confirmed" is way early, because it isnt. You are likely focused on what you can buy now through the Tesla store, which does not necessarily match what people have installed currently. Since they dont specifically exclude previously installed equipment, and in fact specifically call it out as "no additional hardware needed", that should be the expectation for current owners of this equipment thats already installed.