To give everyone here the benefit of the doubt, the first bottle seems to be a pet shampoo for getting rid of mites and ticks (the second is just a regular delicate soap). It could quite plausibly be that the poor thing had a bad infestation and stopped trying to escape when it realised it was feeling better. If that is the case then it’ll be freaked out but definitely better off for it
Cats have an instinctual response to a specific patch on the back of their neck being pinched. Their mothers carry them by that part when they’re kittens, and the response keeps them still. Male cats also bite female cats there during mating. It can be used to functionally restrain a cat, though doing so unnecessarily is just gonna stress the cat out so it’s generally not recommended