Being bored is good. If they're never bored, they'll never have incentive to learn to entertain themselves. I don't think that's the problem, the problem is that instead of getting creative, he throws things.
For whatever reason, your post reminded me greatly of DD's behavior after DS was born. She has never been a big toy player and after the little guy came along I would constantly find the cushions on the couch thrown around the room, sheets pulled off my bed, shoes and coats everywhere, etc. My reaction was WHYYYYYY?? I hated that mess. Toys on the floor wouldn't have bugged me at all, because it would have seemed so normal.
Around that time I read Alyson Schaefer's Honey I Wrecked The Kids and really related to some of her suggestions for preventing power struggles...the theory that a power struggle can be a sign that they are ready for more responsibility. So you give them more responsibility, in an age appropriate way, and with a clear timeline or logical consequence. For example - DD was a huge hassle to get ready. So I told her to get herself
ready, and set up some situations where I told her, and could enforce that if she didn't get ready we wouldn't go or I would leave without her (clearly, DH was home for that one.) Yes she tested, and I enforced, and no more power struggle about getting ready. Anyway, the getting ready thing may or may not apply, but just to give an example of how the technique works.
DD used to be pretty bad for throwing things and creating a giant mess, but I have tried to be really consistent with imposing logical consequences on that - you throw, you clean up. Of course she doesn't always want to clean up, but I usually insist that she does before we move on to the next activity. She has tested me on this but over several months of this she is used to the house rules and understands the expectation. I still have to supervise since she is too young to stay focussed on cleanup, but I do not ever pick up stuff that she throws. Ever. She doesn't throw as much anymore...what's the fun when you just need to pick it up?
DD also does 30mins alone quiet time per day, which has helped increase her toy play and ability to entertain herself.
Just some thoughts, take what you like and leave the rest. Good luck
I hate to say this too shall pass because I'm not naturally patient when I hear it I feel so powerless as a parent, but, um...this too shall pass. He will soon get past the craziness of having his life turned upside down by the arrival of a baby and will have an active baby brother to play with. While you are waiting, just try your best to fit in the self-care and get the help that you need to be patient with your DS!