It fits in my personal item (a small messenger bag), in its case, along with good noise-cancelling headphones. There's space for the other stuff I need (a small bottle of water and a snack), but not a jacket, which I have to wear or tie to the strap. I don't think any personal item-sized thing is going to have space for it and headphones a laptop (I put my laptop in my carry-on, which is usually either a 20L backpack or a 40L ultralight rollerboard). Its case has space for a charger and since my phone and headphones are USB-C as well I can just stick with it. It won't be flat like your switch.

I don't think I'd try strapping it to the outside of any bag, even though the case it came with seems quite good. I think it would be unwieldy.