I am glad DS1 loves his baby brother and none of this energy or 'challenging behaviour' (anything from wilfulness to aggression) is directed at him.
Regarding others: yes, moving into the bigger room at nursery will be exciting and stimulating and he will want to run with the herd. He will be louder to make himself heard yet at this stage he can flip from hearty rough play to tears in seconds.
"I don't allow toy guns or Batman they promote violence" said one mother smugly as we looked past her to where her angelic 4 year old was kicking seven bells out of his playmates.
Testosterone surge or not, at any rate after 3, children get physically more confident and capable but lose control of their tempers.
Address any tantrums or unacceptable actions at once, take a few deep breaths then wade in, try and keep your voice calm and unshouty. He's very much loved, he knows it, you can reprimand him without crushing his spirit believe me. A cool off area away from an audience helps or if necessary cut short a visit, go home.
I found small snacks fuelled them so they didn't get tetchy, but do watch sugary intake. Let them out in tons of fresh air with exercise to wear them out; not likening your boy to a dog but think of keeping a vigorous breed from destructive anti social behaviour.
Is there a safe play area outdoors or softplay indoor facility near you where you can sit with baby while DS1 burns off energy?
Mix playdates with small tasks he can achieve and feel good about accomplishing at home. A specific job like, "Please fetch X" or "Could you please pick up/tidy Y?" That way he looks to you for praise and encouragement so you can focus on positive actions.
He may have dropped a nap altogether, quiet time if not actual sleep can give him a breather.
One friend confided she must have worn out 3 phrases "Indoor voice', "One at a time!" and 'Where are your hands?" with her sons.
At nearly four DS1 is old enough to start revoking privileges, and get pulled up on blatant rough behaviour towards his peers. (The nursery should do their bit to enforce good behaviour when he's in their care, have you asked how they do this?). The main responsibilty for his self control lies with you and DH.
Sorry for epic post, but your son can be sweet and gentle sometimes so all is not lost.