You're not alone op. Many parents have been in your shoes. Of course you will always meet the ones who haven't yet but those who have will understand.
Parenting is a journey of one guilt added to another, and sometimes we don't cut ourselves enough slack. Sleep deprivation is a form of torture in the military for a good reason.
I am not the parent I want to be when I am overtired and I live in guilt with my lack of self control and my ability to get the rage when I wouldn't normally.
Obviously the best advice is to tackle the sleep problem so you're not so desperately tired, but I realise it's not always possible, and in my case I am cruelly tired through medical problems which won't go away.
One thing that's helped me is to reframe my logic when dealing with troublesome behaviour of the kids. I realised that if I am a shouty and impatient Mum they will become accustomed to that and tune it out, so it won't even work. They also model my behaviour which makes me feel even worse. So I try to consciously view it differently and remember that a soft answer is often as good as a harsh one; even better actually as it's not damaging. They seem to respond to it as well is what I mean, which negates the rationale for being too rough.
We're not perfect because we're human. Someone once said to me that a bad parent wouldn't care, so the fact you're bothered by it means you don't need to be worried about yourself.
hope it gets better soon for you op.