I have much anecdotal insight here...
I am a teacher.
I am an August baby myself.
I have a September baby and two August babies.
I echo previous posters’ comments:
My last class had two boys of similar ability born 51 weeks apart. While they achieved similar gcse results, the younger was in far more frequent trouble for silly - not awful, just silly - behaviour. His immaturity showed, right to the end of secondary school.
My own experience was nothing to do with academic success but rather irritation at being the last to: get a Saturday job, learn to drive, drink (legally!) in pubs etc.
With my eldest two children, I see my September baby’s books at parents’ evening (y5), compare them to the younger one’s (y4) and it’s obvious that a difference is visible (very youngest August baby not yet at school). When I look in my middle child’s books and think about what the eldest was achieving a year before, it’s clear that beginning the y4 curriculum aged 9 is a massive advantage over starting the same Work aged 8 and three weeks.
However, what we should all realise is: babies come when they are ready and academic (or sporting) success or lack of it is but a tiny part of who they are. Being a decent, kind person is the main thing. And, by the time you are old, like me, it won’t matter that you had to wait longer to get that Saturday job. People need to just chill on this issue, because there isn’t a great deal anyone can do about it. The way to influence your child’s success, in my opinion, is not when you try to conceive but in the way you nurture them to work hard, be resilient and all the rest of it.