They have some actual features in there like find my buds, music sharing and noise cancellation controls. Also there’s some settings adjustments like standby times, connections and voice prompts. It’s actual pretty useful.
You don’t. The last pair of Bose headphones I had came with instructions to download the app which I just ignored. The headphones worked perfectly fine without the app.
You need it if you want to turn off or change the noise cancellation mode.
There is a button that cycles through high-low-no noise cancellation on mine
Not on the first gen, however, I had no use for the app and deleted it after the first time I played with it. My plan was to download the app whenever I wanted to do something, then immediately delete.
By default the button is set to use voice controls with your phone. The app let's you make it do anc controls
When you buy a new pair these days, pressing that button causes the headphones to say "Configure the action button in the Bose Connect App"