Hey Shannon,
I think you are doing the best you can, and you shouldn't be beating yourself up about all these things. Not "you should feel bad for beating yourself up" (I know what that spiral feels like as I've been there) but you can be kind to yourself. Give yourself grace to not be perfect. No one is punishing you, except you, for these things you're worrying about. You don't deserve to punish yourself with this.
It must be especially hard for you because you were raised in a very religious environment where guilt was constantly being placed upon you, and that would have trained you to constantly be hard on yourself. Unlearning self hatred is difficult, but it's worth it, because the outcome is being at peace in the present and enjoying life. Which is what you deserve to feel.
I know it's easier said than done and changing negative self-talk is NOT easy, cause I lived with it for over a decade and it required therapy and psychedelics to overcome. But it is possible.
Regarding Sophie - you're not a perfect parent. And that's MORE THAN OK because NO ONE is a perfect parent. You are a deeply loving parent who puts their child first, and is constantly thinking of ways to make her happy. That's a wonderful thing, and something Sophie knows and feels, based on what you tell us in your writing.
Regarding pets - it's not a failure to not be in a position to give your child a pet at this stage. Many many parents don't give their children pets, because they live in housing where pets are not allowed, or because they can't afford them, or they're disabled and can't properly care for them.
Maybe when Sophie is a little older and can take full responsibility for a pet and it won't add to your list of duties that are already overwhelming, she can get one. Many pets are outdoors pets, like a bunny rabbit in a hutch, or a guinea pig, or even certain types of dogs. Or even a small pet like a lizard or fish could be a good start. But it doesn't have to be now. As I say, MANY good parents don't give their kids a pet. I didn't get a cat when I was a child, despite my heart being set on cats, because my dad was allergic. It did NOT traumatise me. And we didn't get a dog until we had a property with a very large backyard which was when I was a teenager.
Taking Sophie on trips would be nice, but not taking her on trips will not be traumatic for her. My family couldn't afford to go away for vacation when I was a kid, and it didn't bother me, because my parents made up for it in other ways. It's the same for Sophie, I'm sure.
Finally, as for "bad genetics"? Without your genetics Sophie wouldn't be alive, wouldn't be the lovely child she is. All genetics are a mixed bag - my mother passed a connective tissue disorder down to me, but also her creativity. I would not swap my creativity for anything.