He’s angry and frightened, and this is all completely age appropriate behaviour. He’ll get better with time.
Definitely give him plenty of one on one time. Wear baby in the sling as much as possible, don’t use a bouncer when big brother is around.
When he approaches baby I would prepare to move away and remind him “we’re gentle to each other in this family”; if he leans in, stand up and leave and repay the same thing once, but don’t make a fuss.
Put the dogs bed in another room if this is becoming a habit.
Keep his routine the same as much as possible. Keep boundaries in place - try not to do too much screen time and snacks to keep him quiet (I know that’s hard). Take a firm but kind stance on boundary-pushing in general.
I suppose the main point - be firm, confident, and living. Show him you understand he is struggling but you have confidence that he will learn to be a kind big brother with your support. He’s scared, he needs to know you have this in hand.
This is what we did in the end for our 3 year old, after a few months of misery all round. It helped a lot, and she’s happy again. Janet Lansbury’s podcast might be worth a listen, she talks sense about this stuff in my opinion.