OP, I recognise that paralysis you are in. Looking back, I think I was depressed but didn't see it at the time.
I also worried about my dc in their father's care if we split. Turns out, he wasn't that bothered, didn't want the responsibility, and was too utterly selfish and focused on his own needs to fight for them. So he sees them every now and then but there is no commitment there. With selfish men like your DH, they just cba with parenting. That won't change if you split. They may make noises about court, access etc, but the DC are a millstone to them, to be enjoyed now and then (Disney dad style) but they don't want the day to day care.
A lot of what you said resonated with me, especially the single parenthood while still in a marriage. I figured I might just as well BE a single parent and happy, than stay with him.
The freedom of spirit that I enjoy now is amazing.
I also had to suffer to the shouting, disengagement, lack of sex, selfishness, me doing all the parenting, housework, admin, not supporting me, etc etc. It ground me down until I was a shell of a person. I see that in you now. You barely have any fight in you.
Honestly, it's not just a trope. If you are happy then your DC will be happy. Don't foist on them an adulthood of guilt, bad relationships and therapy because you stayed with their father 'for them'.
Kids adapt. A bit of disruption now for a happy childhood and well adjusted adulthood. Please leave him for them if not for you.