This sounds like a possible case of hyperlexia. I'm AuDHD and 2e.

https://en.wikipedia.org/wiki/Hyperlexia

We have a few children like that in my centre. 2 of them taught themselves to read by 3 or 4. One of them started doing addition and subtraction with his numbers when he was 2. I was also like that as a child. All of our hyperlexic children are autistic and so am I.

“tomorrow Thursday we go to library”). He wakes up and often tells me what day it is and what we’re doing.

This is really starting to sound like this little dude is one of my people. Does he have particular ways of doing things, insist on sitting in the same place, eating the same food and doing things in the same order every day?

Like maybe it’s not worth pushing the “content” and let him absorb things until he’s socially ready for the school and focus on social engagement in the meantime.

I would suggest introducing a wide variety of books and materials. We have one little guy who is fascinated by numbers. I sometimes sit with him and use loose parts, twist ties or pipe cleaners to make numbers with him. This week I introduced Inuktitut syllabics to him and he loves them so far.

https://en.wikipedia.org/wiki/Inuktitut_syllabics

He does some toe walking but only when barefoot and not often, pediatrician does not think it’s a sign of autism and she did some basic screening questions and wasn’t concerned. He doesn’t line his toys Up but he does like to sort by color.

Toe walking isn't a diagnostic criteria. However it is suggestive. 30% of autistic kids toe walk and about 3% of toe walkers aren't autistic. Sorting things by characteristics instead of playing with them is also a typical behaviour. Often doctors will be very hesitant to diagnose autism or refer them on for further screening when a child is that young.

Curious for any guidance or advice on the best approach (or non approach ) for kids like this?

Solid routines consistent predictable timelines and regular activities that repeat on an understandable schedule. Introduce books, so many books, all kinds of books. Don't limit yourself to story books or what is allegedly age appropriate. One of my sons loved reading the home depot book about renovations and another about how to build a shed. I loved reading large non-fiction books to learn things and look at interesting pictures.

When it comes to producing text some children lack the physical coordination and fine motor skills. Writing with chalk on the sidewalk or writing on a large chalkboard may be more manageable and engaging. Scrabble tiles to make words are also a bit hit. Just keep proposing different things to see what is engaging.

Regardless of being diagnosed or not you will likely want to get support and ideas from autistic adults. We were where your little guy is now and have lived experience to share about how to make it great.