FWIW I have had two very domesticated exes. I never lived with the first one but he had lived alone a long time and cooked, cleaned, hoovered, took bins out, did washing, ironed, etc., so men are clearly very capable of domestic chores.
The second ex had lived in a blended family with his ex's children and their shared child, alone for a bit, and then when the pandemic forced us into a sort of live-in situation, he continued to cook, clean, wash up, hoover, iron, etc., to the point where I felt a bit guilty, like a bad house guest.
I know it was not a marriage, but I'd go to wash up after dinner and he'd say "no, I'll sort it, I know where things go".
The only reason that your "D"H is not doing chores is because he Can't Be Arsed and thinks you'll just pick up the slack. I personally would not handle this level of complacency.
PS. Also look out for weaponised incompetence; he might "try" to do more if you really have a go at him, but do it so badly that you end up sorting it out anyway.