Like a couple other posters here, I don't have kids of my own. I was a nanny for many years, however, for many different families and took a huge role in the raising of my two younger siblings from a young age. I love that you're working with her on lists and I think what other folks have suggested about mixing in fun is great.
Kids, like adults, want to feel like what they do day in and day out is important. They love to feel like they have something to offer - whether that's to themselves or to others. Even little ones want to "contribute" in some way towards the work that the big people are doing. For example, when I was a housekeeper/nanny for a big, wealthy family, I had a terrible time getting chores done. I was always being interrupted - the kids just wanted attention always! Then I realized what they really wanted was to spend some time with me, so I started letting them help me with chores. The kids were 2-12, so they helped in ways that matched their ages - and I often had to re-do chores after they'd helped me - but we all got what we wanted. They got to feel like they were contributing to the house the same way I did - and got the same appreciation I did - and I got to move through the chores. It didn't save me a single minute of time or an iota of effort of course, but I felt it was worth it to avoid the stress it caused us all.
When I think about it, doing chores and homework doesn't sound like much fun to me either. But working together can lighten the load and leave room for some fun. For example, maybe there's an audiobook the two of you can enjoy while you work together on a chore. If you have a library card, you likely have access to an app called Libby which will have thousands of free audiobooks available! Forgive the library plug - I'm no longer a nanny but rather a librarian these days.
There might also be some fun programming at your local library where you can let her get some of that extroverted energy out - while you take a break and read in the corner!
You might also see if there's a way to lighten the load for yourself, too. We know that "it takes a village to raise a child," of course, but many of us are working with depleted villages these days. Is there anyone you can lean on to help you with your own responsibilities? Or even just vent to? Those outlets are so important for parents - I wish our communities had more of them.