Wow I am amazed at the responses on this thread. I thought MumsNet was supposed to be a place mums could come to for advice without judgement. Guess not!
OP having a morning coffee while your child is happy in their play pen is NOT lazy! Every parent deserves some time to themselves in whichever way they can get it- as long as babies needs have been met and baby is safe that is all that matters. Would be a different story if baby was locked in playpen all day long and you just ignored baby to do your own thing but from your post it is clear that isn't the case.
There is also so much hate on the screen time too- do people not realise that is the world we live in now. Kids in school do the majority of their work (especially in high school) on screens. Same as a lot of workplaces. As long as their is a mix of screen time, play, reading, walks etc what is the issue?
Both my sons had screen time from a young age (probably a lot more than they should have based on this thread)- all educational stuff when younger that morphed into their likes the older they got.
Both my boys are highly intelligent, great marks, always top of their classes. Since starting high school my son hasn't had less than 100% in any Maths exam (he used to do a lot of math apps on screens when younger)- he's almost finished the 2nd year of high school now.
They are both polite, respectful and behave when out and about. The youngest loves to read and you will often find him drawing or creating a new book. Loves to craft and has an amazing imagination.
They has a LOT of screen time growing up- but we also played together, socialised and taught our kids boundaries and manners. They can entertain themselves when needed and interact with others when needed- they can do BOTH.
So no- screentime isn't going to turn a child into someone with a short attention span that has awful behaviour.
You also then have the opposite- those parents who have had baby glued to them from day one, no screens, nothing and when older those kids don't have a clue how to self entertain, need attention 24/7 and have outbursts of bad behaviour when they don't get what they want because they are used to being centre of attention 24/7. I've seen it in friends children who took a different approach to me- who have even said to me now that they wish they would of done things differently in the younger years.
OP you do what works for you, remember you are doing your best and finding what works for you & your child. There is no such thing as a perfect parent and don't let anyone tell you otherwise. As long as your child is loved & cared for (which it sounds like she is) that's all that matters.