Bose Music App doesn't detect Wi-Fi on IOS 16.3.1 either...maybe.
I had it working on an iPhone SE with 16.3.1
I upgraded to an iPhone 14 Plus and I had it working once, but then I touched the icon in the upper top left corner of the app (which I think was for My Bose account) and since doing that I get the error. I also did numerous times of installation and removal afterwards to no avail.
I can see the sound bar connected on my router. If I shut off the 2.4 GHZ network, it will connect to my 5 GHZ network. If I shut off my 5 GHZ network, it will connect to my 2.4 GHZ network. So, I know the sound bar is talking on my network.
If I shut off the Bluetooth permissions for the app, the app will request access to Bluetooth.
If I shut off the Wi-Fi permissions for the app, the app does not request access to local network.
Hope this helps. For now (knock on wood) I can hear sound from my TV through it, but if I want/need to make changes...I'm screwed.