You're talking about my son
He was exactly like that and all the tests and such showed nothing but a bright young lad trying to cope with big changes in his life. And school is such a big change from his first 5, cruisy years.
At 6 he hasn't got the vocabulary nor the thought processes to to say, 'Well you know Mum, I like school but I have to concentrate really, really hard on everything and I'm not used to it yet, and there's so MUCH to learn so actually I just want to go back to the way I was and play." (or something similar.)
My son was so absorbed in whatever he was doing at home, it was as if he were in another world. He would often no even respond to hearing his name.
At school he could take in just so much - then seemed to switch off.
But as he progressed to 7 and 8, he learned to manage. I hope this is the same for your sweet boy.
We expect so much of little ones, don't we and at 6, he's only just past babyhood, bless him.
At that age they haven't quite grasped self-control in any form and most children will ignore what others want from them when it conflicts with what they want for themselves.
It's a bit early to test for dyslexia but the school can advise on that. Eye and ear problems too.
I'm sure you read to him and encourage his learning so he will grow into himself, as they say and as he sees his peers doing acceptable things, in the sort of time frames expected, he'll learn to do the same.
A short attention span is (sort of) proof that he needs to concentrate and focus more than other kids to get a task done and this can be very wearying and can easily lead to the sort of inattention to bodily functions as you describe. It did with my boy.
If you're worried, try not to show him you are but maybe talk to the school's counsellor, if they have one, or the Principal, usually an experienced teacher who's seen it all.
It worked out just fine for my son and I'm sure it will for your dgs too. 