Hi Pruni we moved when ds was exactly the same age as yours and I do believe that the repercussions were actually a lot deeper than I gave him credit for at the time. Ds also left a beloved childmnder and group of friends. Tbh honest I was so wrapped up in the move (and new baby) that I didn't think through the effcts on ds nearly as well as you are.
One tip we followed was to sort ds's bedroom on moving day before anything else so he had the same bed, toys, even posters on the wall in more or less the same position as his old room when everything else was still in chaos. it did really help for him to have sanctuary.
The other tip - be prepared for some retrograde steps. Ds was well on the way to being potty trained and went right back to square one after the move.
Good luck!