Reading your updates, YANBU. I have psoriatic arthritis which causes pretty bad fatigue and I'm in pain a lot of the time, so I do have some understanding of what he's going through. My condition suddenly appeared about 6 months post-partum and looking after DC is no joke. I manage to work, contribute to household tasks and look after my son, I just do it a bit differently.
If your DH was so severely unwell that he couldn't manage caring for himself etc (as some PP describe) then my advice would be different- he can only do what he can do. But if he has capacity for lengthy socialising, he has capacity to be involved at home IMO.
My take is that he has to prioritise when using the energy he has- that's going to take willingness on his part and a bit of creative problem-solving. His DC and you need to come before socialising, but you may also need to structure your days differently to a family where neither parent has a chronic illness.
-If finances permit, is there any scope for him to change his work to something more flexible? I freelance, and pace myself throughout the day- short burst working, short rest, 2 minutes just making something in the house slightly better. My energy is often very low, especially in the mornings, so that might mean literally wiping down one worktop. I repeat this work-rest-clean cycle all day, and get a surprising amount done while feeling much less tired that I would hitting one task hard (I know I'm extremely lucky to be able to work like this. But maybe pacing might help him when he's not working- splitting cleaning into microtasks with rest in between instead of longer chunks).
-Accepting that house is not going to be perfectly tidy. Everyone is fed and alive, that's good enough for me.
-Meals are simple so nobody's time is spent cooking anything complex. Pre-cut veggies, we eat a lot of salad vegetables to cut down on washing up, low-prep meals like jackets and beans, and I batch cook when I am having a good day so I have quick, healthy meals ready when I'm feeling bad.
-Systems for everything to make every household task as low-effort as possible. Dishwasher is a lifesaver (we got a cheap one from Facebook)
-Playing to each person's strengths. I can't lug a hoover around the house but I can organise finances. DH prefers physical work over mental work. So we split responsibilities to suit each other's abilities.
-not relevant to you now but with an older DC. I find it helpful to have lots of tabletop activities on hand that I can do with my son but that are manageable sitting down. Lots of magic painting, board games, sticker books etc. We pace ourselves through the day- something more active, sitting down activity, very short burst of cleaning, repeat.
-To be honest, if he does have some energy (sounds like he does) then he needs to give what he does have to his family and his social life gets what's left. Of course he can socialise but he really needs to priorities his family if he has limited scope to do stuff.
None of this is meant to mean that people with disabilities should 'just get on with it'. I also understand that his condition probably affects him differently and apologise if my advice is totally irrelevant. But he sounds similar to me in that he has some ability to do things around the house/care for his child. In that case, it is his responsibility to commit to finding manageable ways of doing things.