Im a mum of 2 SEN children.
It is totally normal as they grow up for their sensory needs to change, my eldest used to bath almost daily, then had a stage where it was like id suggested she bathe in cats urine.
You've had lots of good advice already but i just wanted to add a couple of things.
NT people tend to see things as a whole event. Im gonna have a shower. Whereas with ND the process is more, gather the motivation to do the task, then its putting the water on, finding the temperature, then taking your clothes off, getting in the shower, and im not sure if your son might be thr same but here we have the issue of not being able to wash straight away, so its getting used to the shower, the temp, humidity, direction of spray, etc, then washing. Then rinsing, then getting out. So its not just getting in the shower, in our minds it become a job with 10 steps. We've had issues because all of these steps feel overwhelming, and its not just "jumping in the shower" its a combination of steps.
Have you tried different times of day for showering? You might find mid morning is a better time than early morning or later.
Me and my eldest cant stand having the "big light" on when we're bathing, we either have the door open a crack or a little light on if its charged 🤣. We have a chargeable light in the bathroom that has different colours too. Also music/a programme on, audio book make a difference.
Also we have a shower over the bath, and a sit down shower is great sometimes.
Ill see if I can think of anything else 🙂