A couple of random thoughts come to mind, reading your story. Just for background, this never happened to me.
In your telling, there is an obvious connection between having everything of 'his' removed and him starting to pee everywhere but the toilet. Since taking away everything seems to have started it, I'm not sure how it is logical to take things away to end it.
3yos are not capable of lying, because they don't understand that there is a difference between what is real and what is not. Their brains are not developed enough (and won't be until around 7) to know these are different. Just as a 5yo will think 'I killed my baby brother because I wanted him to not be alive,' a 3yo is incapable of discerning truth from preference, fantasy, imagination and pretend.
This is one reason for promising to do one thing and having no way of following through. But children are not legally able to sign binding contracts, and it is mostly because they do not understand the term 'binding' in any practical way.
Children are well aware of the fact that they are at the mercy of their parents, and have no way of entering into equitable negotiations with them, which drives them uncontrollably to 'say anything' to gain approval, cooperation or security. He gets that you're mad at him, and he can't cope with that reality emotionally, so he'll say or do anything (in the moment) to make that stop happening.
Children have a very keen sense of ownership, so your lad can't understand how something can simultaneously be 'his' and you be allowed to take it away. If it's yours, it's yours to control (take away, give back). If it's his, you've stolen it.
I would suggest reading Alfie Kohn's book, Unconditional Parenting, for an excellent explanation for why punishment and control simply do not work. It's not that they're bad or wrong tactics, it's that they are universally ineffective, and every single attempt to control another person, even if it appears to 'work' in front of your face in the moment, will have unintended consequences like those you are experiencing.