If it's just piano then it's basically Muzak. The bus itself may even be playing some imperceptibly which you can harmonize with.
I've tried headphones with babies before and it's hit or miss. One would howl instantly if you put them on him while another loved them.
Seems like you found the least intrusive way to keep your kid calm, which I think most people will appreciate.
I feel for you, man. Thank you for sharing. Hopefully you feel a little better after letting it out.
Are you seeing someone about your anxiety? That seems like the primary issue. My spouse is a stay-at-home parent while I work full time and I still have all the responsibilities on your list. It's often stressful, but that's being a parent. If it's pushing you into anxiety attacks then you definitely need to address that first.
You'll also have to be clear on your limits. If she wants you to organize playdates and you don't have any time left then make it clear they won't get organized. There are only so many hours in a day.