Humming, singing and hyperfocusing - anyone

[HiyaFelicia]

We've adopted a (now) beautiful two year old who came to us last June at 18 months. He's a very happy and very (very) active child who loves nothing more than running. Oh and climbing of course. Although it's still early days we want to ensure we do the 'right' things and try to be as proactive as we can.
The transition from FC was very smooth as we had a protracted intro including 14 bump in meetings in a park as well as daily video calls for months due to his FC having to shield. So when he came to us he was very familiar with our faces and voices. He slept through the night from day one 🙌
He's been with FC since he was born. She has adult children and had to shield for a long time. The only child he really interacted with was FC's granddaughter, who is a year older.
When we take him to the playground he shows little to no interest in other kids, not even the ones who follow him and try to say hello, bless 'em. Some of the parents however are greeted with 'Hi!' Or 'Bye bye!'.
His speech is delayed, he can say two words clearly although occasionally he will say a seemingly random word out of the blue but won't repeat it even when encouraged to do so. Like lady bug the other day. Other than that he mumbles. He doesn't point at anything to explain what he wants, for instance a certain toy or if he wants food instead or a drink when he says 'nam nam'. This can be frustrating for him for obvious reasons. He can't sit still for more than five minutes unless we read to him or when he becomes hyper focused on a small toy like a Duplo block which he will fiddle with for ages and look at from all angles. When he hyper focuses he's almost always humming the same part of his favourite nursery rhyme (Twinkle Twinkle Little Star) over and over again.
He's been going to nursery for three weeks now and they are due to write a report. Although they did not seem to have any major concerns they did suggest that they were going to spend some one-on-one time with him to encourage his speech.
Does anyone have any experience with the humming, singing and hyperfocusing?

Our wee one did this (came to us at similar age) where he would just seem to zone out and be very engaged with something, often a leaf / crack in pavement or mixing something. I assumed it was hypervigilance and that, needed us near but in his own head space if that makes sense. I think it was a version of the freeze response ( fight flight or freeze) and he did it lots again when he started school and after some other stresses. We did lots of ' wondering' with him to help him recognise it as anxiety. We are many years in now and have no specific issues, but he still does a subtle version of it as a coping strategy when anxious, trends to fidget and zone out if asked a question he can't answer - in schoolwork for example. We are working on how to overcome this for exams in future! Hope it's useful to know you are not alone even if you don't think it sounds the same.

Thank you for your reaction and sharing your experiences. Your explanation does make sense. Giving it some more thought it feels like maybe our lo's humming/singing could somehow have some sort of soothing effect on him(?). It is the same bit over and over again so it's almost like a pattern/cadence. Maybe to self regulate a sort of coping mechanism?
We have contacted the la's child psychologist for some guidance and he's on the waiting list for SALT re. his delayed speech so we'll see what the professionals say.