Maybe it's the social structures that aren't wired for men to do it, rather than the biological ones. What made you feel like the difference was biological rather than due to external society?
The second is that when my youngest was 6 months old I felt nothing for him. I saw a psychologist about this and they said it was really normal for dads to not feel connected to second+ kids until the kids are past a year.
Single parenthood is even harder, it sounds that you have done good job with them.
Just that the a lot of those frustrating and isolating aspects are not that you are less made or less capable for it, it is shared frustration and depression. Tho, advantage of being mom is that you can find other mom to complain to. I agree it is harder for men who are less likely to be in that position.
Hormonal things are more after birth. Moms can also get "touched out" when you don't want touch anymore. Some of cuddling is really done because you know it is good for kids.
I don't want to be the one who will say your experience of being uncomfortable more does not exists. It is way more ok for women to touch other women them males touching other males. These aspects are much different between genders.
Imo, a lot of women specific socialization is really about teaching women how to break isolation etc. It is the thing I realized only after I had kids. A lot of stereotypes were actually adaptation.
I'm not sure if I changed, or it's simply easier for me now they're a bit older, but over time I had merged into this parenting role really well. My kids are both happy and well balanced, other kids and adults both like them and they're doing really well at school.