For some DC with additional needs, yes, it is normal to need to be supervising all the time. For some, it is normal to need to be within arm’s reach at all times.
Request a home OT assessment. This can help you make the house safer for DS and better meet his needs.
If your area offers sensory OT support, worth pursuing that too. But not all ICBs commission sensory OT support.
Housing wise, are you in a rented home? If so, is a council/housing association home or a private rental? Have you considered a disabled facilities grant? Could your toddler move into one of the other bedrooms with one of his siblings?
You should request an EHCNA yourself. On their website, IPSEA has a model letter you can use. DS doesn’t need a diagnosis. It doesn’t matter DS masks at school. You can still get an EHCP. If DS had more support at school, home life would improve too. What you are experiencing is known as the coke bottle effect.
The school should be providing support now. DS clearly isn’t OK in school. Otherwise you wouldn’t be experiencing the coke bottle effect. The school just isn’t recognising the signs or is recognising them but not recognising them for what they are.
Request social care assessments. On their website, Contact has model letters you can use. Also look at your local short breaks offer.
Contact Home Start to see if they can support you.