OP, does she always have issues with this, or are there times when she's a bit more aware of her hygiene?
Since you've mentioned there may be a neurodivergence/sensory processing component to this, I wonder if it might be related to her executive functioning and/or vagus nerve. If she does have issues around exec functioning, sometimes straining on the loo (or other stress) can cause a temporary impairment in a person's ability to manage all sorts of things, from remembering to do things, motivation, interoception (interpreting bodily signals accurately), organisation, motor skills, curbing overthinking and anxiety, etc.
Plus, the fact that you say she has accidents because she's too engrossed in other activities sounds familiar to me - my DC (now teens) have ADHD and ASD, and they had similar issues at that age around both sensing when they needed the toilet and in switching tasks to actually go to the loo. It was never as simple as "receive signal, go to toilet, clean up" for them. Plus, rewards didn't work to motivate them as it wasn't that they didn't want to do the right thing (their toileting issues were a huge source of frustration, stress and shame for them, especially around school) - they were simply perplexed by the whole thing, their brain wasn't receiving the right messages and then their exec dysfunction meant that it wasn't handling messages in an appropriate way anyway.
If, looking at the bigger picture, you think that she might have ASD/ADHD/sensory processing disorder or similar, I would speak to your GP and ask them to refer her to CAMHS for assessment/support. There will be a long wait, but there are plenty of things you can try to improve her exec functioning (diet, exercise, sleep, routine, etc) in the meantime that might help with toileting - everyone is different, so it's a case of trial and error even with psychologists and other professionals involved.
Also, this sounds a bit silly but have you tried different types of toilet papers? My DD wasn't aware that there were different options at that age as toilet paper was just toilet paper and I just bought the same kind every week, but now she's a teen and has more life/toilet roll experience from hotels, etc, she refuses to use anything other than a mildly quilted aloe vera one as it's the only one that doesn't feel like she's wiping her bum with sandpaper! When she doesn't have that, she will have a bath after every bowel movement as it makes her feel sick to use the other textures of loo paper.
Another option is one of those plastic bidet bowls that fit over the toilet so she could clean herself with soap and water afterwards, but DD was absolutely horrified when I suggested this to her!