I asked this exact question during a primary school open day last week. The head teacher was very reassuring and said they have a few children in Reception class who are still in nappies, some with SEN but some without.
Our 3.5 year old is partially potty trained. Attempt at the start of summer was disastrous and our child was extremely distressed and was withholding for such a long time that we were worried about a UTI developing. So we backed right off.
A couple of weeks later, our child suddenly said they wanted to use the potty! We didn't push it but tried again a few weeks later and they were in pants after a couple of days with only a couple of accidents since then. Slight regression since starting nursery. Our child is extremely stubborn and has unbelievable bladder control so can hold on for 6 hours!
They still poo in their nappy at nap time though. And night dryness depends on when their brain reliably produces enough anti-diuretic hormone, so not in anyone's control. So I'm not worried about their continuing to wear night nappies for a long while yet.
Don't feel bad. All you can do is try and if it doesn't work, back off for a month or two to give them more time to develop, then try again, and repeat as necessary. The Princess Polly/Pirate Pete book worked well and lots of stickers.
Good luck! And remember there's nearly a year before they start school next September and a lot can happen in a year at that age.