This question has been asked a lot so check out other answers too.
In the interest of clarity, I propose addressing the underlying problem and not just the symptoms. The problem is that your son's needs for belonging and significance are not being met, this is further aggravated by the arrival of a new baby that forces him to question is his place in the world (subconsciously).
Parents must be really intentional about meeting this need for a child (and any person really) to feel like the belong in the family/group and to feel needed/significant. In Positive Discipline, we call it understanding the (subconscious) belief behind the behavior and is based on the work of Alfred Adler originally. Here's a further description I wrote here.
Thus, to promote his self-reliance and therefore ability to play independently you must meet these needs for belonging and significance.
To meet his need for belonging, one thing I would try is to be really intentional about carving out time to spend with this child without any distractions. Schedule it in advance, let him pick the activity, and name it his mommy/daddy time. You know your child best so do some brainstorming with your co-parent to think of what would help this child feel the most connected/wanted/etc. Have this time away from the infant. (As the infant grows, s/he will need their own mommy/daddy time).
To meet his need for significance, give him opportunity to feel needed and capable. This can be reached in part by helping with the baby, but his identity needs to be more than just a big brother. I really like Balanced Mama's answer to a related question:
If you are folding laundry hand him some washcloths and let him try his hand at folding. Yes you will need to go back and refold, but in the meantime he is learning that you value your time with him AND that you value his contribution (a REALLY important lesson that helps with a lot of things later on - including discipline). Laundry also makes for good "matching" lessons and opportunities when it comes to pairing socks. Also importantly, he is learning social skills as you speak together. While you talk about things that are NOT toys and games, he is learning about how to learn, how to listen and the give and take of language.
In the kitchen, give him something to stir or mash or knead (great life skills to know and sensory experiences). It is a good sensory experience for him, he learns kitchen skills from watching you and the two of you can talk about what you are doing which also helps him build his vocabulary. You could also put a little water in the sink and let him "help to wash dishes" as you make them (just don't have any knives wind up in his reach). Dish washing is another experience that teaches him a life skill AND gives him another important sensory experience.
To address the playing issue more immediately, try investing time teaching him how to play. If he is the first-born and doesn't have a lot of experience with imaginative play, this is especially crucial for his own development, as well as your sanity. I responded here. Basically, slowly take his play one step further by asking questions and introducing new scenarios into the game.
To respond to the tantrums in the moment you have many options, some I have used are:
"Let me know when you are done."
"Wow, you are upset/angry/frustrated. Let's cool down and then we can talk" (this works best when you've already brainstormed with him options to help him calm down, and as a bonus it helps build his emotional literacy when you name his feeling so that soon he can begin to name his own feelings so he won)
"I need a hug" (I love this one, it stops them in their tracks and helps you both feel better!)
"My ears hurt when you speak/scream like that and I can't listen. Let me know when you done screaming so I can listen"
Toddlers want to be heard just like the rest of us. But unlike the rest/most of us, they don't have the language skills nor the emotional literacy/regulation to be able to communicate without screaming. These are the skills you must teach your child, with the same care, attention and patience as you will teach him to read, use the toilet, etc. It is no different. Giving your child attention won't cause/reinforce tantrums, it will help prevent the need for them. If you're only paying attention to your child when he throws a tantrum, that's a different issue.
As always, my favorite blogs for this are:
Can We Hug It Out
Parenting From Scratch
Single Dad Brad
And, if you need a laugh, and it sounds like you probably do, here's a blog written from the perspective of a toddler that I just found yesterday. It is very funny!
