My toddler is 3 in June and I have an almost 5 month old and the behaviour is quite similar, solidarity not much advice
He is obsessed with his wee brother but can be rough and handsy, he sees us tickling the baby they he goes and tries but is like rag dolling him about
when he is over stimulated I do noticed then he will go out of his way to hit the baby so we've really pulled back on screen time, what he's watching when he does watch it and I got a wee timer off amazon so he only watches 30 min chunks twice a day.
I got little routine cards which help so if I'm about to feed the baby or put him for a nap I'll show him those for baby's now and next and then show him his now and next like you playing your toys now, next mummy and you will play etc. Also of he's really over stimulated blowing bubbles helps them regulate breathing and calm down.
Usual stuff as well like trying not to have a big reaction to when he hits the baby, Lots of one on one time etc.
Who knows some days and weeks are better than others. What doesn't help is him and his wee pals play so rough at nursery, sure it's normal but it means he wants to play rough and tumble with everyone so really having to work on that boundary
Just adding would a wee picture book of you all help? My sisters a community nurse and works with families and kids who have ASN and she has really good tips and tricks and that was one I haven't used yet as we go through pictures on our phone before bed of the day but a wee photo album might help with the separation anxiety? She also gave the blowing bubbles advice and speaking in now and next rather than over whelming them with plans for the whole day x