That all sounds really normal. Mine doesn't really play with dolls and stuff now. Its all about drawing and activity books and reading.
If you want her to do some self play, you might need to trick her 😉
I lure mine into playing sometimes by leaving half done stuff around, like ill start a (kids) puzzle and do a few bits and she will join in or see it in the morning and start it or I'll leave a lego in the same way. Or I'll start doing something at the kitchen table and pretend I'm stuck and need her help to do a job and then make us a drink, which turns into cleaning the kitchen so I'm around but not doing the activity.
I also have toys in her room and sometimes ill ask her to do something she doesn't want to do, like tidy her room, and that usually guarantees an hour of play 😆
Another good one is having a clear out for charity - suddenly they will play with that stuff to prove it should stay!
Bathtime. We have a shared bath on a Sunday and I get out and leave her in there to play with toys. I sit just outside so I can keep an eye on her but I can also have a hot drink and read quietly.
Basically, dont worry. She sounds fine, it's just a tough age. Too old to play, too young to want to be alone.
It sounds like yours does loads of activities like mine so we do no tv in the week and unlimited (quality) TV at the weekend, as long as she is actually watching it, not flopping around on the sofa. That obviously has to fit around going to the park or family plans and if she is clearly bored by it then it goes off. My view is, if I was doing 30 hours of school a week, plus walking there and back, 3-4 evenings of activities and probably a monthly big club session, plus homework, I'd be absolutely exhausted so if she wants to recharge watching telly it's fine by me. She is doing everything she needs at school and is well behaved so I'm not too concerned what her activities are.
Eta - we take the approach of saying yes e.g. to tv, until it becomes apparent that there is an issue and as soon as we spot the signs of boredom or a poor behaviour pattern from watching certain shows, we apply the brake, so banning certain shows or restricting tv for a while.