The audio engine on the iPad version is infinitely better than on the desktop app. I can connect/disconnect bluetooth headphones while the app is open and it all just keeps on working. Never had a problem with sound, unlike on the desktop version. Whatever you did here, please migrate that to the desktop version.
Audio setup on iOS is much simpler than on macOS because there can only ever be a single audio device active at any one time. Things get a lot more complicated on macOS! But please rest assured that we know the difficulties with things like Bluetooth headphones that unhelpfully present identically-named input and output devices to the OS are important details and we do plan to make further improvements in these areas in future.