New school sounds like a much better fit for her, hope it exceeds expectations and she loves it there :D
Finding the right educational fit is kind of critically important and it will never be a one size fits all.
one of the problems with the learning culture is that they make it "fun" for the kids in the early stages, gamifying the experience, but not teaching the skills for doing the repetitive, boring work required to actually be better than basic at something
I'm going to extremely strongly completely and utterly disagree with this with the very strong and obvious bias of having been a homeschooler and currently being a coach drawing from my very statistically insignificant sample of three kids that I homeschooled directly, interacting regularly with a wider community of homeschoolers and my rather small groups that I coach with their fluctuating yearly populations but being able to see the development of the ones that have stuck around (basically from childhood to adulthood in some cases). I have and continue to gamify whatever I can/be bothered doing (I can theoretically gamify everything but some things would take more time than I have), and it very definitely teaches the skills to do the work as it's still the same repetitive and boring work done in a much less boring fashion.
If/when they're mature enough to realise that they need to do repetitive boring work quite regularly in life (and some people never do) most will either figure out how to go into a meditative/zen state, backburn if it's menial (think about/plan something else) or gamify it.
There's a bit of scientific evidence supporting play-based learning which I remember doing a lot of research on aeons ago when I was starting homeschooling. I of course never have anything on hand because one of the many things I can never retain is "might need this later" so I never save/reference things which were a passing interest at the time. You could start with the Wikipedia article which has a million references down the bottom if the interest took you (which is probably where I started).