Yes, but not all of those 24 pins are used, and some of them are duplicated.
I also don't think you can make this "main wire" distinction: you shouldn't be counting the power wires if you only care about USB data in the Type A case, and you should arguably be counting the CC wire in the Type C case if you want to go for "strictly necessary to function", or the SBU wires if you want to go for "carries data at nontrivial speeds".
The "12-wire" count of the parent article refers only to the main wires, i.e. the 4 USB 2.0 wires + 4 differential pairs for USB 3 or 4.
Similarly, the "8-wire" count for Type A connectors refers only to the main wires, i.e. 4 USB 2.0 wires + 2 differential pairs for USB 3.