YMMV but I don’t really feel an impulse to try to pin down a single overarching reason why Charles decided not to go to his afterlife. I think motivations are messier than that.

I think he was afraid while he was dying, and Edwin made him less afraid; I think he was afraid of going to an unknowable afterlife and Edwin offered him an alternative.
I think he’d fought so hard for every inch of joy he could get and didn’t want to give it up, and he had dreams of a better future he’d never gotten to see come true, and this wasn’t the same as getting to live, but at least he could still see the world he should have gotten to grow up in.
I think Edwin had been kind to him, and Charles makes friends easily, and going off with a kind person who wished they could have been friends for longer felt better than facing the unknown alone.
I think Edwin was a light for him on the darkest night of his life, and Charles, who wants desperately to be a hero, to make a difference, to help, latched onto that and decided that was what he wanted to be.

I don’t think you can nail it down to one thing. Motivations are complicated and all exist at once, and they shift and change with time and circumstance.

Charles tells the Night Nurse that he’s here because he still has a purpose: he’s a dead boy detective. He tells Edwin that he’s not going anywhere without him. Maybe those reasons aren’t why he ran from Death in 1989, but they’re why he’s running now.

My bias is that I don’t tend to be as compelled by the idea of love at first sight, or soulmates as something that happens to you. I’m more interested in the idea that you can capture someone’s attention quickly, but love is something you build. Charles and Edwin spent 34 years building a life together. If they’re soulmates, that’s why.