Those thoughts are very common. Take a deep breath and let me offer some assurance from the other side of the parenting spectrum.
I made some great choices as a parent when mine were little. And I dropped the ball completely on others. But 85% of the time I was flying by the seat of my pants and using common sense plus desperation to come up with solutions and just make things work at the moment.
Screen time wasn't a parent issue but rather a survival one - because either I needed a break or because I desperately needed to finish a task / help another one of my kids.
I tried to greet them with a smile every morning and every time I saw them and do all the little things to make them feel special (up to and including figuring out how to cut PB&J into hexagons because they got tired of the squares/triangles options). I read to them, took them on trips to zoos and museums, engaged them in summer learning projects, and spent what feels like half my life helping them memorize math facts.
But I still had times I yelled at them, let them sleep all night on the floor in their clothes, signed off on "mandatory reading minutes" that we never did for homework, got impatient and didn't let them finish talking, let them eat dessert first and on at least a few occasions declared McD french fries an actual meal. And I banished play-doh from my house simply because I hated trying to clean it up.
In other words I was (am) a normal mom. Very good in some things, very bad in others, and eh-okay in most.
But here's the thing - those little ones of mine are now adults / almost adults. One has her master's degree, another her bachelor's degree - both married and own their own homes. Another is graduating a world class university this spring and got a job offer tonight for a starting figure higher than either my spouse or I have ever made in our lives. The fourth is in an honors program at a different private university and is an Eagle Scout. The remaining two in high school are both in college prep classes - one got an award last year for their kindness towards others, the other one for their leadership of a new club they formed.
They are all doing just fine - not just by my parent bragging, but by outside standards - they are doing fine. Not because I did everything right - but rather despite me making a mess of many things.
The three keys - they were loved. They were shown how learning is important (and I can still recite at least 12 children's books by heart from the number of times I reread them). They were always allowed and encouraged to be themselves.
Do your best and set your anxiety aside. You care enough to worry about being a good parent - that's already makes you one.