@Pira progress is about far more than academic progress or behaviour. Sadly schools often say DC don’t need/won’t get an EHCP, but parents go on to successfully apply themselves. Not all with ASD/ADHD will need an EHCP, but you have nothing to lose by applying.
The provision in EHCPs is taken from assessments so what is included depends on them. From your posts I would suggest OT (including sensory OT) and SALT (which is about more than the ability to speak) would be helpful.
Also things like regular movement breaks, a wobble cushion, sensory bands on chair legs or exercise/peanut ball or a rocker/bouncy chair, time out card, social skills support, instructions written down, checking DS has taken in instructions, placement within the classroom. You don’t need an EHCP for these, but the only way of guaranteeing it is via an EHCP.
Even without an EHCP the school must make their best endeavours to meet a pupil’s SEN, which is about far more than just behaviour and academics.
The EHCNA also often highlights hidden needs because no one can truly know all needs without a comprehensive assessment. To give an example, everyone thought DS3 had an excellent memory, and he does have a superb long term memory, but that was masking a very poor working memory that was contributing to some of his difficulties.
An EP assessment would be part of an EHCNA. Personally, unless money is no object now I wouldn’t seek an EP assessment prior to applying because if e.g. the LA agree to assess but not issue any report will be out of date by the time you get to an appeal hearing. Reports used to be considered up to date for around 2 years but over the last few years SENDIST have considered reports much younger out of date. It may also be that the LA’s EP is OK but you need to prioritise independent SALT and EP.