Weird, I'm the exact same way. I can concentrate perfectly fine in a coffee shop, but at home it is difficult unless I have absolute silence and total solitude. The presence of one person (even if they're not bothering me) is enough to completely derail my ability to concentrate. I think it's because in the back of my mind, I know that person might interrupt me, and just the "threat" of interruption is enough to prevent focus.

I wish I was like von Neumann sometimes. He was known to do his best work on quantum mechanics in the living room with his whole family sitting around talking and the television blasting.

I have a feeling that quite a lot of people are like this... If the study hasn't been done yet - I'll contact some researchers I know who would be willing to do the study. Anyone here is welcome to help design the experiment. I'd recommend tracking a few more variables including EEG, pulse, w/ & w/o Adderall, w/ & w/o caffeine, ... Just brainstorming for now.

One aspect that probably plays a role: I'm feeling good because I kept busy, but I've been pretty isolated due to an extended health issue (heavy metal poisoning) that takes loooong to recover from (but it works fine thanks to chelators), and I deliberately work a low-paying job from home. While I'm not an extrovert I'm no introvert either, I enjoy talking and even presenting and got very little of that the last few years. So the reason I go to the coffee shop is - people. While I don't talk to anyone (because that only very rarely works here in Germany) somehow just being in the crowd feels good, it satisfies some deep desire. Somehow merely having "noise" at home, even if the source is people, is not the same. The brain is not that easily tricked, it knows the context. It's more complicated though since having people talk does help even at home, but it's different, different brain circuits are exercised, it's not a replacement for the 2-3 hours in the coffee shop.

Perhaps on some level you believed you were performing for an audience?

It can be a confidence builder for me to "successfully perform" in a noisy, busy setting. Perhaps someone looked at me working just now, but I didn't flinch! Knuckling down and blocking out the world in a setting like that may help get you into the productivity zone.

I've noticed that in my open office plan just putting my headphones on helps me concentrate, no need for music. I know others will be less apt to interrupt me because I have signaled to them that I'm shutting them out and getting work done. I can devote less awareness to others and more to my tasks.