As the owner of various cats over 50 years it does nothing to adult cats. It will hurt an adult cat because their weight is too much for the skin to hold. As a kid I tried it many times because I heard the myth and it only made my cat more angry.
I don’t believe kittens are affected other than being physically unable to do anything. Sort of like if you were put in a half-Nelson hold. You wouldn’t be catatonic, just unable to fight back.
As an owner of a less cats over less years, this is absolutely a thing and is sometimes referred to as “disabling” or “deactivating” the cat. You can do it at home with a clothes pin.
You don’t pick them up.
Here’s an example from what looks like a professional setting. https://youtu.be/T9TmmF79Rw0
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A clamp (padded, preferably) on the scruff of the neck will temporarily brick a cat.
To be fair, he wasn’t talking about picking the cat up by the scruff of the neck, only squeezing it there.
Anyway, regardless of your anecdote, it is a real thing: https://www.cambridge.org/core/journals/animal-welfare/article/pinchinduced-behavioural-inhibition-clipthesia-as-a-restraint-method-for-cats-during-veterinary-examinations-preliminary-results-on-cat-susceptibility-and-welfare/CFCC52F39F2235340C1DBA4630EC07F0
