Help me with my parenting guilt

I'm a stay at home parent with chronic health issues and I'm currently recovering from quite bad burnout. I have 90 minutes a week paid work and obviously all the normal house stuff to do. My plan over the summer holidays was to have my children both in 'childcare' two days a week so I could get my work and house bits done in those days. This week I wasn't able to organise anything for my 6yo old. Nevermind, I thought, he can just hang at home while I do my things. But I feel so guilty. I feel like if he's home I should be engaging with him. Or organising activities for him to do while I'm busy. But I don't have the energy/capacity to do more on top of what I already do. My brain is just convinced that because I have the privilege of not having to work a full time job I should therefore dedicate all my time to parenting as that's my job. On top of that he's very hard to settle unless the TV is on. He uses it as background noise, tending to play, build Lego or do colouring while it's on but it's still on. So I feel guilty about that too. Growing up I don't ever remember playing with my parents during the holidays so why has this expectation become so pronounced for me? Do other parents feel like this and how do you manage it?