You have all my sympathy it is a difficult phase.
Overall, It sounds like you are just exhausted and need a break and that is why this hyper part of the day is wearing you out. Is there anyway to get a bit of extra help for a bit, even say once a week at that time of day?
Remember it is a phase, whilst they get used to being at nursery, at four they are developing and growing fast and trying to take in lots of things at once.
I had two hyperactive ones.... And I think the above pp re den building is worth a shot.
They def are holding it in at nursery And at pick up time they had to let it all out.
I used to have to give them food immediately on pick up as they would get hangry. It did make a difference.
Can you take him home on a little scooter (with a lead or something if necessary) or stop in a park ( if you're both well wrapped up) to let him jump up and down outside for a bit - weather allowing. Otherwise, the shops where they could choose a small something. We often used to go to a large garden centre where they could walk around looking at Xmas decs.
I remember buying a mini fitness trampoline, that they could jump up and down on indoors ( had to put bubble wrap etc round the edges... but that used to help. And foam balls to chuck about did less damage. Building a cushion fort would have kept mine busy, they would have enjoyed the idea of taking everything off the sofa and hiding. Or playing with big cardboard boxes. with blankets over them. I think you can buy tunnels which fold down again.
Having food ready or planned the night before as there was little time to prep meals when they were on the go and I had to keep an eye on them. Once they had eaten and were still sitting I used to swap the food with playdough so they could fiddle with that.
The bath with plenty of toys and an audio book on also used to help, familiar songs or stories. I used to clean the bathroom at the same time.
Its hard to build a routine when they are constantly on the move, but it does help. As does moving to different rooms.
Are there any weekend sports clubs or swimming lessons near you for his age group. We did mini rugby from 4. It can be quite relaxing sitting on the sidelines for a bit.