I am in practice and this is not how we treat our apprentices. If I saw members of my team tutting and huffing in response to questions I'd pull them up on it. Not acceptable.
You acknowledged caseloads - we have times where we are very overloaded, but that's not our apprentices' fault. Worse case scenario we would find them some work they could do with a little less input while we dug ourselves out of a hole - but otherwise, we make the time for them. It's important.
So please don't think any accountancy apprenticeship would be like this. Size of the organisation and culture will be factors in finding somewhere that has better skilled staff in training her and a more supportive culture.
Somewhere big enough to have an intake of more than just one apprentice at a time - and that has a proper HR dept running apprenticeships - might be a better fit as they are more likely to have the skills and culture to support her. She'd also have more peer support if she's got a few fellow "first year apprentices" around not just older ones who've been there a while.
(For instance, as a rough sense, I'd expect a lot if not all places in the top 50 practices would meet that measure, I expect places in top 100 would too, and maybe outside it. But that might give a starting list of practices to research? I wouldn't necessarily suggest top 10 as those are very pressured cultures and don't sound like they'd suit her - but for her to research.)
I agree with pp that AAT is the right starting point for a 16 year old. It's giving people the grounding and adjustment time to the workplace etc. Our apprentices do 2 years AAT then can move on to an ACA/ACCA contract if that's right for them. I wouldn't be trying to go all the way to L4 AAT necessarily unless that's all she wanted to do.
Online learning is hard, but there is usually an element of self-directed study expected from our apprentices too. It's not about abandoning them, it's more that learning to direct your own learning is an important skill to progress in accountancy as in future she will need that for the more advanced exams and to be confident to do her own research on client's technical points etc.
It's better if there is also some 'real' time at college with people too, but having an allotment of self-study time in the office each week is possibly not unusual.
There is no harm in her requesting regular one-to-ones with her manager. In an ideal world they'd have initiated that, but sometimes managers in practice assume if it's not requested then it's not wanted. (Realistically, most managers in practice are promoted based on their technical and client skills over their people management - it's not a lack of care for staff they just may not appreciate she needs it.)
Maybe goals can be to find a few ways to make getting through L2 more manageable (e.g. 1-2-1s); weigh up seriously how much of this is 'grass is greener' looking at her friends / culture shock (the first 6 months in any role are an adjustment); research other practices that take on apprentices to identify a short list and start applying? Also think about long term - is the plan 2 year apprenticeship and move to chartered training contract (ACA/ACCA) at 18?
What is the exit on her contract though, how much will she have to pay back? Sometimes a new employer will cover that but possibly less likely at this level.
All of that said, sometimes we have apprentices who realise that actually "accountancy is not for me, this isn't what I thought it would be" and they leave to do something entirely different.
Whatever she decides next, it was a really brave step to take on an apprenticeship at 16 and she should be proud of that.