Children do not need a diagnosis to qualify for support, either in the classroom, or for exams. What is necessary, as you have indicated OP, is evidence from testing in school, perhaps from outside agencies and examples of it being the child’s normal way of working.
All of those things will probably be long term. The child will have been identified as requiring additional support in whatever way and strategies put in place for support.
The school should be speaking to parents about the need (or not) for additional time, reader, scribe, rest breaks etc al, but parents will not be applying for them. As you work in Learning Support, you should be familiar with any pupil who requires support and evidence of need and the SENCo will coordinate written evidence and the exams officer and SENCo will apply for whatever adjustments are deemed appropriate.
I don’t see why parents need to be worried about the JCQ regulations. They need to have conversations with the school if they are. It would be surprising if most pupils didn’t have long term support in school, to accommodate their need, whether learning differences, ND or both.