It's SUCH a hard phase.
Locking him in his room for a very short time (2 minutes?) as a punishment for actually climbing on the baby is one idea. But beware that you don't want him to end up thinking that being in his room is always a punishment, because that'll make bedtimes hard!
Put all the energy and strategic thinking you can manage (through exhaustion!) into prevention. There are some great ideas earlier in the thread.
Focus mainly on the 3 year old. You can chat to him even whilst dealing with the baby and looking at the baby, because the 3 year old understands the words and knows you're paying him attention, whereas the baby is happy to be looked at/cuddled/hear words.
"Big brother, you used to roll around too when I changed your nappy. You were such a funny baby and I love that you're a funny big boy now and we get to giggle together every day!"
Big brother can choose a book that you read or a game that you play whilst you feed baby. He can choose baby's outfit when he chooses his own.
Taking on a new "project" with the big sibling can help. We worked our way through the Tickle Fingers book with baby sibling on my back if fussy or playing on the floor or in the high chair if happy.
My three year old loves his new solar system sewing kit and his train set and matchbox cars. They'll keep him happy for long enough for five baby feeds.
My now five year old needed the climbing frame or cushions as stepping stones or likewise.
A little playpen in the garden can keep baby safe but still mobile, while big brother cycles or climbs or digs.
On walks or time in parks, big brother can be given a challenge (build X out of sticks and mud/ find the best or biggest leaf / spot an insect) whilst baby has a few minutes out of the pram or carrier. Picnics help with this if you can cope with the chaos and mess! Any meal is more fun when it's outside, somehow.
You'll find your way through this difficult phase. And using it to engage your 3 year old more and make him feel even more valued will only pay dividends in future.
And when you feel like you've mastered this phrase, the next one will start 😉