Am I making too many mistakes as a nanny, or am I just still learning the family’s routines?

I’ve been working for a new family for about 3 and half weeks as a nanny for one child. My employer is actually very nice, upfront, and understanding when she gives me feedback. She communicates what she wants clearly, and she hasn’t been rude or mean to me. I think the bigger problem is that I’m becoming increasingly nervous and anxious about making mistakes, and every time I get feedback, I worry that she’s going to think she made the wrong decision hiring me.
For context, I’m used to working in a very fast-paced nanny job with two children, so I’ve gotten into the habit of rushing and trying to get everything done quickly. This family has different routines and expectations, and I’m still learning them.
A few things have happened recently:
Laundry: She gave me feedback about making sure laundry is completely dry, checking the dryer, putting away clean clothes that were left in there, and making sure damp clothes/bathing suits dry before going into the hamper. One day I was busy cooking and didn’t check the laundry, so some things weren’t finished. She also recently explained exactly how she wants the child’s clothes folded and which drawers certain clothes belong in. I thought I was folding them neatly, but apparently she has a specific system she prefers.
Dishwasher: I also made a mistake with the dishwasher. I put something in/handled something incorrectly because I misunderstood what should be done. She pointed it out to me, and I felt really bad because it was something I should have been more careful about.
Dog walk: Today she asked me to walk their dog for 30 minutes. This was my first time ever walking the dog, and she hadn’t given me a specific route, usual bathroom spot, or routine beforehand.
The dog wanted to go a certain way. When I tried going a different direction, she stopped and wouldn’t move. Eventually she sat down and then turned around and led me back home. The walk ended up being about 15 minutes instead of 30. She also spent most of the time sniffing and didn’t pee.
My employer told me that the whole point of the walk was for the dog to pee. I felt terrible because I didn’t accomplish what she wanted, but I genuinely didn’t know where the dog normally goes or what her routine is.
The thing is, my employer is not treating me badly. She’s actually very nice and understanding, which almost makes me feel worse because I really want to do a good job for her. I’m just getting more and more anxious about making mistakes, and now I feel like I’m constantly doing something wrong.
I also know that I have a tendency to rush because of my previous nanny job, so I’m trying to slow down and be more attentive.
I’m not looking for people to just reassure me. Please be honest with me: am I being careless and making too many mistakes, or is this fairly normal for someone who has only been with a new family for 3 weeks and is learning their specific household routines?
And if you were in my position, how would you stop yourself from becoming so anxious every time your employer gives you feedback?