I teach year 2. The most important thing for children this age is family and what goes on at home.
Can I ask what is going on at home - do you read to him every day, several story books every single day? Do you go to the library? does he read to you (5x a week, pref every day, just a few mins), do you play board games (good for maths), do you cook and bake (again maths), do you have lots of enriching activities for after school - colouring, drawing, play dough, creative stuff? This is what makes a difference to kids.
and talk. Talk talk talk. Think aloud about everything in the world. Look at that pink flower? Where do you think that cat is going? What do you think will happen in this story?
you are right, in that the squeezed middle gets the least attention. But we do look at all children and what they need to do to push them on. If he is having phonics interventions then you could do more of this at home but in a fun way just through reading. Even story books, he can try to recode the odd word, follow the story with his eyes as you read. A little and often, every single day. In a fun way, through stories, not through boring phonics cards. It’s very very dry and he is getting a lot at school. Supplement and complement with stories and as much reading practice of his school books as possible.
and also as little screen time as possible. Just a bit of CBeebies if you have to. Attenborough. Enriching tv that teaches them something while they relax, not Netflix shit. Pref not American as it does affect their language and how they say things, their vocab, so stick to UK stuff while he is learning his sounds.
the more fun but engaging stuff you do at home, the better. We find that our children who are avid readers are also excellent writers because their vocab is so rich.
For absolute sure he would get more attention at private school. But there is so so much you can do yourself that will make more of a difference and cost nothing but a little time. School is already intervening, they have noticed, they have a plan. Ask what you can do to help. And don’t panic. He will be fine.