Separate from the phone and screen time discussion, you are at an important juncture of your life, a transition to parenthood that could change everything. I say "could" because I fundamentally believe that half of people who have children don't have the self-awareness to change and adjust their habits and emotional state.
One of the monumental realizations for me when I became a parent (not necessarily the first day but over the first 5-7 years) was distinctly what my parents did right and wrong. My dad told me on the phone one day that I shouldn't show my child my feelings, that I should hide any negative feelings and only show positive feelings. And now I see that this is what my father did to me and it constrained my ability to share negative feelings with my friends and family, instead leading to me bottling up negative feelings like anger and sadness.I realize that this is not the correct way to parent, your child should see the full range of human emotions from their parents and although you want to be careful to not put too much emotional burden and stress on them to create an anxious child, you want to also be sure they see you at your best and worst. They should see you discuss your feelings with others and with them and when you lose your temper, as we all do, you should also afterwards rationalize what you were feeling with them, apologize if necessary (and it's usually always necessary because there is no need for any human to lose their temper with another human that's been on the Earth for only a few years).
Any way, I think of parenthood as a journey of self-reflection and improvement, much like childhood. Just like some people have a negative painful childhood, parenthood can be similar. The goal for you is to be open and honest with yourself and your growing family, and to be constantly looking for ways to improve.
Apologies if this sounded like a lecture but wish you the best in what may turn out to be the most important job of your life.