I was really concerned about this, ds is born late June and has speech and lang delays and is generally 'immature'. He's currently in reception and will be on an IEP (individual education plan) by the end of the year, meaning he will get lots of support hopefully in Yr 1. Whether this is due to his summer birthday I'm not sure.
My ds is also massive for his age (99th percentile, aged 6-7 clothes and tallest in class!), I call him my gentle giant lol. But the teacher and speech therapist have said to me it's easy to forget he's a summer born and expect more of him based on his height.
My ds is behind in literacy - can't read/write yet and many of his peers, particularly girls can. BUT in my experience working in schools this is standard despite age, teachers sometimes need different approaches in their teaching to boys and girls imo.
I think the trick is to get them simply enjoying what they are learning about, so instead of pushing my ds to read, atm at home we are focusing on me getting him interested in books, choosing fantastic stories and bringing them to life. I made alphabet cookies, we play lots of online games for phonics etc... And the teacher said he's come on faster than she intially expected.
Good luck OP, I am sure your ds will be fine, this time last year I felt the same as you. Make sure you establish a good relationship with teacher too, I meet with ds' once a term to catch up on where he's at and what we can reinforce at home. Also best advice is don't panic if/when talking to other parents saying their kid can do xyz, ok my ds can't spell 'cat' but he can build fantastic things, is fearless in parks/monkey bars etc and is a bright kid.