Look OP I get it, I’m a pushy parent too 😆 (but not rich enough or near to any schools who do a 4+ exam). But honestly, phonics summer camp?? As if 3 year olds will focus all day on learning sounds?
I did teach my child to read at 3.5 (I’m a teacher) but she was at a nursery that taught a sound each week in preschool year (which I don’t think your child is in yet) which helped and she was keen, and we just did a few minutes a day, then once she could blend we did a book each evening before bed for 10 mins.
Yes she is a fantastic reader now in y2, but she was bored in R and y1 as the school didn’t differentiate at all. She got wordless books for half a term in reception, then books with CVC words for months, by which time she was reading chapter books at home. It wasn’t until half way through y2 she brought home reading books vaguely near the level she could read at.
from what others have said actual reading isn’t required for the 4+ anyway.
and yes, it is amazing how quickly they start actually reading once they start learning. The order of teaching is planned carefully to make sure this happens.