I've never suggested putting her back in nappies! Even through all of my daughters accidents we kept her in knickers, she went into school with a spare set of clothes in case of accidents. She started school with a toddler diarrhea and food allergies diagnosis both of which can impact the notice she gets for needing a poo. So we were planning for accidents before the issue with the teachers arose.
Teaching every need is a multifaceted approach it can seem like using the toilet is a simple thing but there are lots of factors.
You need to understand what the toilet is for and why we use it - if they were previously dry this they already know
You have the ability to recognise when you are about to wee - sounds like they already have this
You then need to learn to recognise the signs so that you can get to a toilet without having an accident. This can be where some kids start to struggle. - it can be they don't recognise early cues, it might be that if distracted they don't pick them up
You then need to be able to get to a toilet - physically getting to the toilet is one thing, feeling comfortable going into the toilet room is another. We have plug in sensor lights so the path to the bathroom lights up as you walk past so she can see and she has a stool so she can reach the toilet light.
You then need to be able to sit and relax the muscles to wee/poo in the right place. My daughter is very small for her age, despite being 5.5 she's only the size for a 3 yo so she needs a stick on seat to make the toilet seat small enough and a stool to put her feet on.
That's the process but things can complicate it. If you are frequently having soiled accidents you are more likely to develop a UTI which then makes it more likely to have wee accidents.
If you are feeling tense or stressed you will struggle to wee you might only release the pressure of wee and not empty the bladder. Resulting in needing more wees, losing their sensation of a partially full bladder meaning it's only when it's really full you have that signal to say you need a wee. The more desperate you are the less time you have to get to the toilet.
If you are anxious and worried you might have to work yourself up to asking for the toilet or going into the bathroom these eats up into the time between your brain saying "I really need a wee" to your body going "I can't hold this in any longer"
If you are constipated or previously have been constipated the bowel expands and you lose the sensation of a full bowel and don't know when you need to go.
My daughter is now in y1 and I would say that there were a handful of other students in reception that had the occasional accident and there was another girl that had frequent accidents in the first term. My daughter had a good second term and rarely had an accident but once the warmer weather came and the school upped the water they were getting them to drink she started having accidents again. This was when they started lowering the barrier to communication and she's not had an accident since. We had more of an issue with the school changing her than they had but as long as the frequency of accidents was dropping we were less worried.
We have worked on language too, so the teachers would ask "who wants to go to the toilet before PE" rarely would she say yes, they now tell her "you need to go to the toilet before PE". They used to do forest school outside and would be told "go to the toilet as you won't be able to there" she took this to mean that you aren't allowed to ask to use the toilet and not that there wasn't a toilet readily available. They now say "there isn't a toilet where we do forest school so go before hand so you don't have to come back to the school". Like a lot of 5 yo she takes words quite literally!