Sounds like he uses every trick he can to get out of doing stuff with/for his child.
Another misogynist who thinks kids are women’s work no doubt.
He gets up late every morning so everything’s done by the time he appears.
He stays on the phone at lunchtime so he can’t be asked to do anything. He spends hours in the toilet so again he has peace.
He wants an hour if the OP gets an hour to lie down alone.
However he does some things so he can justify his behaviour by saying that he does this or that, as though that ten minutes somehow makes everything ok.
All tactics to get out of doing stuff.
During the day he can’t be expected to do very much as he is being paid to work, however if asked, and not in an online meeting at the time, he should be able to parent his own child for the four minutes it takes for you to go to the toilet FFS.
Before work and after work dc are both parents responsibility. Remind him that he’s not pulling his weight out with working hours and you need a rota as you’re not doing everything, it’s not your fault there’s covid, and you’re not putting up with his laziness any more.
Remind him that if you split up he will have to take dc half the time so he’ll have even less time to himself so stop pissing about and do his share.
Then take a day each at the weekend and you leave dc with him and leave the house. For as long as possible. If he complains just tell him that hassle is what you have to put up with during the day so now you know how I feel. It’s hard work. You need to do your share mister. There’s two days at the weekend and you’re doing one.
I’d also refrain from sex, due to his comments about not wanting another child, as no form of contraception is 100% and you can’t risk another pregnancy with Mr lazybones. That should provoke a response. It’s the truth though.
Start arranging the ducks. Copy his bank statements, P60, pension info, wage slips etc. In case he decides life apart is preferable to parenting his child. Unlikely but you never know. Keep yourself right in case he kisses you about, as he apparently has little respect for you.