My dd is a year older than yours and she asked to homeschool when she was younger. It wouldn’t have worked for either of us, she’s very outgoing and would have hated not constantly interacting with other children. She, however, likes small and cosy environments and I suppose felt safer at home and there were lots of stress triggers, many of which have eased as she ages.
She changed from a smallish primary to very large state secondary and it was a big jump. Lockdown was a relief in some ways and despite being fundamentally a bit lazy, she did all of her work from the lessons despite there being pretty much zero live lessons. Your dd otoh doesn’t seem to have done this. It could be that she found the work too hard or laziness etc. My dd needed a lot of help in the first lockdown in year 7. Some of it confidence and wanting a ‘buddy’.
What I suppose I am saying is that you could perhaps look at the reason behind your dd not wanting to attend school. Friendships, bullying, the school itself, or she struggling in her learning etc. I had a quick glance at online private learning, because let’s face it, you don’t have time to homeschool and you want her to have a broad education, you’d have to pay and I had a quick google. For example, Cambridge Home School is 9k a year and works very much like a traditional school, just online. Otherwise it’s tutors or Oak National Academy, which is going to also be expensive or a hard slog. The latter of which will be very boring and lessons often go over the hour, meaning she’d be working longer to complete than a school day, albeit there would be little homework.
Perhaps set her up a school day on Oak National Academy, mark her work when you come home and see if she wants to homeschool then…
Perhaps you will get answers from parents evening. When my dd had parents evening at the end of yr8, the child the teacher were discussing at her school was so different from the person I know. She wouldn’t ask or answer questions in class, so minimal participation and after I discussed this with dd, I realised she was very stressed in class. Fine in the playground hanging with her mates.
If your dd has a particular need, for example is stressed, there are options to get the school to work with her and help identify issues in class, to make a few tweaks to help her feel more comfortable. You could also (subject to funds) get her some private tuition. Perhaps with students if you have a local university. There is a learning hub near us where the classes are taught primarily by students. And I hear very good things.
I get you wanted to give yourself time to think, which will also have both given her the idea she was being heard. But the double edged sword is that it will have given her the thought you may be swayed. So if you can identify the issue, perhaps you can tackle this together and even if nothing changes, she will at least be heard.
As for the laziness, give it time, it only clicked with my dd just before she went back to school in year 9. Things go up a notch as the groundwork is lain for GCSEs. Year 7 is a big jump and it takes a long time for the children to settle in. I’ve read schools don’t really expect much learning for the first term as there is so much learning going on outside of lessons, ie getting to grips with the new school environment, orienting themselves and so forth. Lockdown meant this process was interrupted.
My dd asked this school year to change schools, which she has now done so. She chose a smallish independent, rather similar in feel to her primary. I get that isn’t an option for everyone. But if it wasn’t for her, I would have worked with the school and filled in the gaps with private tuition.