He sounds exactly like my exH. He gradually checked out of all aspects of family life and marriage, supposedly because of work.
He worked away from home half the the time and when he was living at home he spent all his time in his home office. When he was home he was too busy to leave his desk to eat with us, so I usually ate alone with the kids.
Like your H, he was too busy / tired to have sex, go out without the kids, go on family days out or date nights. I wouldn’t even ask him to do anything around the house.
Every time I talked to him about it ( about every 6 months) he would either blame me and there would be a huge row or he would promise to change and he would do nothing.
So if I asked him to spend some time with the children at the weekend , he would sit on the sofa watching the Grand Prix, drink beer and fall asleep . Then claim that he had given up his valuable time to be with the children and they didn’t what to spend it with him.
If I ever asked him to take the children to an activity, he would be very late or do something else wrong to spoil it for them and ensure that I never asked him again. Eg took son to a football party, dropped him and drove off with sons football boots, kit and birthday present in the car, so son couldn’t join in the party.
He never ever bought a single birthday or Christmas present for me or the kids, I had to do it all.
Every single time we went on holiday he would leave part way though to work. Once he left me in Greece alone for a fortnight with 3 kids under 6. Another year we went to Turkey and he didn’t actually leave but he billed over 110 hours on the 2 week holiday.
On the days he was actually there on other holidays, he would work or sleep most of the day then join us for dinner, where he was short tempered with everyone. It was clear to the kids that he resented even that hour and a half he spent with them every evening.
So once the children were school aged I just went on holiday without him.
When the children were small and he came home from work, they would run to hug him and he would literally push them away and run to his computer to check his email. Because he has not been able to check it during the 15 mins it took him to drive home from work.
So eventually the kids stopped caring when he came home. Sometimes he would be abroad with work and they wouldn’t notice for a week.
On the odd day he spent with us eg Christmas Day, he would be “ tired “ by lunchtime and go upstairs to “ sleep “ with his lap top.
He got very very stressed if he couldn’t check his phone every few minutes eg when we were at a wedding or a funeral. He didn’t go to my fathers funeral because he was too busy .
In the end there was no marriage left. was just a unpaid housekeeper and nanny. He destroyed all the feelings I had for him. I wasn’t even upset when we split up.