I didn't have S2S after my EMCS either. No one suggested it, she was handed straight to her Dad. I was in quite a bad way and didn't see or hold my baby until she was cleaned and dressed.
My milk didn't come in either and despite trying really really hard, DD had to be given milk from a bottle otherwise she would have starved! I then had to have very strong antibiotics at 6 weeks as my CS wound was infected, so even though I had eventually managed to pump a tiny amount to add to her bottle (and it really was just a tiny bit, maybe an ounce a day) that had to be stopped too. I was very upset about it all, so I completely understand where you're coming from OP. I felt I hadn't been able to give birth properly or feed my baby myself.
I was very disappointed with the birth. It took me a long time to get over it but DD was fine. Over a decade later, we're incredibly close, so the lack of S2S hasn't had any impact on our relationship. I'll never know if lack of S2S stopped milk coming in, but I've since been told that it's giving birth through the vaginal canal that triggers breast milk, so obviously I didn't have that!
All your feelings are valid, as PPs have said, it could help you to have a debrief of what happened so you can stop asking yourself why things happened a particular way.
Congratulations on your new baby 