You don't have to use their app for day-to-day usage via Bluetooth, however, they make it impossible to initially setup noise canceling functionality without the app.
I'm extremely grateful that the Bluetooth protocol is broken up into specific functions, so I know that if I connect my headphones/car/etc. via bt audio it can't also send data to the cloud through my phone.
Not sure I’d be so trusting. “Bluetooth offers so many options for deployment that developers don't necessarily have full mastery of the available choices, which can result in faulty implementations. “ from Bluetooth's Complexity Has Become a Security Risk [0, 1]
And now we’ve got folks discussing “Using Web Bluetooth to communicate with Bluetooth devices” [2, 3].
See also https://www.theregister.co.uk/2019/11/26/bose_firmware_borks...
Christmas shopping is coming and I sitting on the fence regarding new headphones, but I'm really unlikely to buy Bose now.