OP - when was the EHCP issued? By law, an EHCP has to be reviewed every year. This process includes a formal meeting with parents/carers, the school/nursery SENCO, plus professionals who work with the DC. Has this ever happened?
When a DC with an EHCP changes setting - eg from nursery to primary school, there should have been several transition meetings with the new teacher, SENCO etc. Did this happen?
It may be that the EHCP is very new, in which case, do make sure you know the law around what's meant to happen when. There's some good info here:
https://www.ipsea.org.uk/pages/category/education-health-and-care-plans
That aside, in terms of getting your DS assessed, firstly, as you say the wait times are very long. Why not get him on the waiting list and see what happens? By aged 7, things may be a lot clearer.
I'm sure all this has come as a shock to you and it's a lot to process. My DS has autism and it look a long time for me to come to terms with it. Your lovely DS is still the same person with or without an official diagnosis. My DS tells me that he's grateful for knowing why he struggles with some things. It's not a perfect comparison but someone with diabetes still has that condition with or without a 'label' and knowing that they have a condition means they can get the support they need.
I would also say that most DC with autism do develop and learn new skills - just like all children - but it can take them longer to do so. Many have what's called a 'spikey profile' - so for example my DS is very knowledgeable about his specialist interests but can't tell the time or tie his shoelaces at 15.
As others have said, the priority is to ensure that your DS getting the help and support he needs to thrive now, regardless of a diagnosis. I would make an appointment to speak to his teacher and the Senco. You need to go through his EHCP line by line to make sure it's fit for purpose (any wording like 'would benefit from' is meaningless) - and then to ensure he's getting it. I would say that given his speech delay, you need to really look at what provision is in his EHCP to help with that. (My DS has daily speech and language therapy written into his EHCP for example.)