The v2 part here really just refers to the fact that it's version 2 of the specification. Consumerrs only need to know the term USB4 and the speed that their device operates at. It's sort of like complaining that the ietf has terrible naming schemes because HTTP is defined in half a dozen RFCs with 4 digit numbers. This versioning is just meant for people developing USB things.
Actually this article here is one of the few times where even mentioning the version 2 part is reasonable since the details of these specifications actually matter to kernel developerrs. For everybody else it's just USB4 80 gbps.
Yes it was never intended that any consumer hears about something like "USB 3.2 Gen 2" that was strictly internal naming for people developing USB devices.
In fact the naming guidelines we're simplified even further than in the older version you linked: https://cdn.arstechnica.net/wp-content/uploads/2022/09/USB-IF-language-usage-guideliens.pdf
But yea borderline fraudulent manufacturers and uninformed tech journalists are to blame for all this confusion