Critical success and failure has never applied to skills. It was only ever in the rules for attack rolls and (in 5e) death saving throws. Critical success and failure in skill checks is probably an example of the Mandela Effect. Anyway, for the above reasons I don't use them as such. However, on nat 20s I might provide a "path for success" where one may not otherwise have been possible. But it's never a given. More of an opportunity for roleplay.
Yeah, everyone is very aware it's not in the official rulebook, other than in the section of the official rulebook where it says not to treat it as an official rulebook and only something to fall back on if you can't think of something better.
And for anyone that for any small moment of time may not have temporarily been aware that skill crits isn't in the official rulebook, that problem is solved very quickly the second they meet any other player online.
It's not in the rules, but it makes sense. It also does have rules about taking an automatic 10 for low DC stuff, which you usually only do if even a roll of 1 would succeed so it gives a good trade off having nat 1s be a failure even in skill checks when the player opts to roll instead of taking a 10.