Hi OP, congratulations on the adoption.
My DS is nearly two and has no difficult history or separation anxiety. Even so, he hurts us quite a lot - 99% of the time it is accidental and par for the course with all the climbing and monkey business, and very occasionally he will get a naughty look in his eye and bite us, or hit me on the top of my head. Occasionally he will try to put his hand down my top and have a grope, and has a habit of pinching/twiddling the skin on my chest, left over from when he was breastfeeding. I'd say he comes to the loo with me about half of the time.
I think your DS is a normal two year old, and I'd try to avoid reading too much into his behaviour.
I remember when I first had DS feeling slightly overwhelmed by the physicality of it all - the constant holding, touching, physical need he had to be with me (and of course feeding). It is quite a transition going from an adult social environment where obviously physical touch happens, but not all of the time.
I don't bat an eyelid now, it has been so long that I have had that physicality in my world that I would positively miss it now. I think you need to give yourself a chance to get used to it, it is one of the nice things about having someone so little who needs you so much.
In terms of discipline, be careful to make sure that you are only disciplining him for naughty behaviour.
So, cuddling you, constantly touching you, sitting on you, wanting to be carried is all perfectly normal and not something he should ever be punished for. If this is partly due to some kind of separation anxiety, I would cuddle away until he's more relaxed.
There's then a grey area when it comes to horseplay - DS climbs all over me and DH and of course we get the occasional kick to the stomach, pulled hair, accidental headbutt etc. Most of the time I will go with the flow and just have some physical fun with him, accepting that it's a bit rough but that it's not intentional. But if he's really hurting me or getting wildly excited, I will tell him firmly to be gentle and distract him with something more calming (eg jigsaws).
Also if you do lots of physical exercise with him - long walks, playground, football etc etc, then he's more likely to want to be quiet when he comes home.
The naughty step is reserved only for properly naughty behaviour, like the odd times he bites me even when he's had a warning. He hates it, I hate it, but it is the quickest way of getting him to stop doing something which is properly unpleasant. I know it's going to be harder for you because you will worry that disciplinary measures will damage the bond between you and him, but he sounds like he's all up for bonding with you. Honestly I think all parents feel an element of guilt when disciplining their children, it's not nice when they are upset. But better in the long run!