Jesus bloody wept. These schools will feed you any bullshit and I wish so much I could convince mums to realise how much they will be lied to, fobbed off and gaslit before they have to experience it to see.
This is quite typical for us all with SEN kids.
So, you need to become a little more assertive now. You get gaslit so much you get a bit scared of saying anything. But your instincts are right. Your child absolutely is ND and I know it because you know it. And you know better than anyone.
You need to email the head, copy in SENCO and class teacher. You say with absolute certainty, we believe strongly that Johnny ( child) is ND. We believe both ADHD/ASD. Don't explain why. Just express your certainty. You then request that he be placed on the SEN register. You request that in being on the SEN register, all staff are informed that he is suspected ND and therefore certain accomodations needed.
A key accomodation you would like to request is for movement breaks. Another accomodation is extra support via the TA. Another accomodation would be support in the form of sensory gadgets ( you are happy to provide). It would be best to have a meeting in person to discuss the specifics of these accomodations with the SENCO. Can they let you know when they're available. You'd then like to see these agreed accommodations in a plan. Even a scrappy piece of paper will do OP. These things must be in writing. Conversations over the phone etc don't usually cover it.
If there's any way you could afford a private assessment? I know it's impossible for many. You don't actually need the diagnosis for them to go on the SEN register but they may lie to you about that. Our primary SENCO lied about alot of things like this before I had to research and learn.
Movement breaks, check ins and fidget gadgets did help my son in primary. He was given separate spaces for tests and SATS. The school fobbed me off so badly at first that my request for NHS assessment was declined. We paid for a private one in the end. It's so wrong I know. Child has 3 ND conditions and still they gaslit me. This tells you all you need know ref what you have to do.
The detention thing is not great really but your child is not on an equal playing field so this needs pointing out. They just want you to go away. It's a lot of hassle for school with minimal resources and understanding ref SEN needs.