Can you afford private speech therapy? NHS referrals are so delayed and it's really worth getting that kind of help ASAP. If not a possibility, then at least get onto the waiting list. Stress the school readiness aspect to GP if you need to convince them to refer. If you happen to have a lot of money to throw at things then OT is also worth considering, because they look at the whole development of the child and see which things aren't quite developing on time and do exercises designed to support that. If that would be a stretch, look at the book "Raising an in-Sync Child". There are checklists right at the back with "typical" development so you can see which bits your child might need help with, and then you can go back and read the bits where it suggests activities. It's probably best to get it in paperback rather than kindle and use some sticky notes to mark the relevant pages. All of the activities are fun and just feel like games, my DC are always asking to do "Bubble challenges".
And in general throw as much of the following, totally free things at him as you can manage.
Outdoor, "big" (gross motor) play (climbing, running, bike/scooter/etc)
Being read to - stories, rhymes, picture books, songs, factual books, interactive books, absolutely anything. Don't worry about whether it's appropriate for his age, as long as he's interested just keep reading.
Play with other children, in smaller groups or 1-1 if he struggles with larger groups. If he needs close adult supervision to manage these interactions, keep them shorter and stay close by, but don't avoid them.
Real, meaningful "work" ie chores or other helping around the house (e.g. help to carry shopping, learning how to perform "adult" tasks like looking for items from a shopping list, or putting on a load of laundry.
He sounds fairly similar to DS2 at that age, he is now 8 and diagnosed with ADHD. We suspect ASD but he wouldn't cooperate with the assessment, and suspect dyslexia but they won't assess for that until next year where we are. He does attend mainstream school and can just about cope with it with medication. He can be challenging, I won't lie, but the main adjective I would use to describe him is quirky. (I think he is brilliant, but I am biased of course!) I think long term he will be fine if we can navigate him through childhood and adolescence.
Several of the issues you mention sound related to difficulty with sequencing and planning to me. Something which helps us with this is using things like a visual schedule or prompt card, where steps are represented using images and they can see which order they are meant to happen in. If it is overwhelming or confusing to see all of the steps at once, then being able to cover them and reveal one by one, or swap them out using something like blu-tac or velcro can work well as well.
We are abroad and the school system is different to the UK. I think UK school system may have been kinder to him in some respects, our one seems to expect mad independence from children who are only about six, but the vvvv early start on phonics would have been no good at all. He only just started to develop phonemic awareness (which is the thing they need to work out before they can learn to blend - breaking words into pieces so recognising things like rhymes and starting sounds) about a week after his 7th birthday, which was luckily about 3 weeks before he started school. Delaying the school start was absolutely, 100% the best thing for him. I thought he'd struggle with learning to read but he took to it like a duck to water. I think if he'd been expected to start that at 4 or 5, it would have been a totally different story. So his writing/reading is very poor for an 8yo in the UK, but it's passable for a child in the 2nd year of school where we are. (I am not worried about this - my eldest also went through this system and can read/write perfectly fine despite it being on a later timescale than UK schools.)
YY agree 2yo sounds ahead (not unusually so, typical for a bright child) and this is probably making the difference seem even more stark. What can be tricky with even typically developing 4yos is that most of the time they are very good at memorising long chunks, so they can often recite the alphabet in order, or numbers up to 20+ but they don't always understand the relation of numbers to amounts, ie how to count. Being able to count up to 6 is good, and I suspect that you are able to see this separately because his difficulty in recalling the order of digits outside the context of counting means that he isn't "masking" a lack of counting ability (not sure if I am explaining this well).
I get the sense that for DS2 he is just utterly uninterested in learning anything that doesn't have context for him. For about 6 months before he started school he amassed a vocabulary of around 40-50 sight-words he could read simply because he had memorised the first and last letter and the rough length of the word (most of these were tram stop names) - of course that meant he frequently mistook other similar words for the one he wanted, but it also meant that he was really excited about learning to read and because the phonemic bit came into place just at the right time, it all clicked for him. But then you try to teach him something which doesn't have context and it's almost painful for him to stay focused - he will be almost incapable of preventing himself from slithering to the floor and making animal noises, or using every square inch of his workbook to draw a complicated diagram or something instead.