i seem to be getting the impression that you're just expecting your 14yo to gain independence by osmosis.
Yes, the anxiety levels are unusual, but what have you done to help her work through them other than ask her to do stuff and then seemingly get annoyed when she says no?
Sure, using the checkout is 'common sense' but have you stood there and talked her through it/shown her, then gradually let her do it by herself bit by bit until you could stand back and her do it while you stand by her side and do it all by herself.. then repeated that until she's confident? Then slowly stood further away while she did it herself?
What have you done to encourage her to go places on her own without you? Even if its just next door to deliver a card? Or a walk to the post box to stick a letter in? Why would you assume just because she is 14 and you have a newborn, that she's suddenly going to develop this amazing independence and be able to help you by doing something she has NEVER done before?
Kids don't just learn stuff without us teaching, anxious kids certainly don't without plenty of input and encouragement to help build their confidence.
I don't think you're a crap parent at all, but you need to learn how to parent a teenager, not just abandon teaching them thinking they can learn it on their own.