I don't think it matters too much what you do when, some DC are early birds, others are night owls, some need more sleep than others, some sleep better after a relaxing bath, others like a shower to wake up, some are messy eaters so it's best to do breakfast before they get dressed for school 😂 Routines are good though as they reduce stress and arguments. It's also good to have a mix of structured activities and chill out time when they can do what they want. Like a PP said, if they are busy, they don't have time for screens so it doesn't matter if that's what they choose to do in their free time. I don't see that it matters if your DD watches TV in the morning if that is what she likes, it doesn't make you late, and she does other things in the evenings.
When mine were that age, they needed to wake up before they were hungry so they showered, got dressed, then we had a relaxed breakfast and chat together before heading to school, maybe a quick recap of spellings on spelling test days.
After school, the rule was as soon as you get in (whether that was after school or after extra curricular activities), lunch box goes in the dishwasher, school bag is unpacked and repacked for the next day along with PE kit/musical instruments etc, school uniform out for the next day.
Then we had a snack and chat in the kitchen (a packed snack on days they went straight to an activity), followed by any homework/music practice/chores (just things like loading the dishwasher/putting laundry away/feeding pets at that age). Some DC might need a rest before tackling homework though. They would have dinner with us later in the evening. They did about 2 or 3 evening activities at that age, some after school, others later in the evening after homework etc. We did some lift sharing so quite often they would have a friend over on activity nights. That worked well as they would play together rather than sit in front of the TV. Once homework/activities were done they did as they wished, play, watch TV or play computer games, have friends over...
Bedtime and story was about 8.30pm.
If you want more structure, less screen time but extra curriculars aren't right for your DD at the moment, you could set aside time for regular activities eg a board game night, play dates, walks, craft/baking/cooking night etc. At that age, one of my DC's friends used to cook dinner with his sister once a week (under supervision).