You only need the app to adjust settings like EQ, turning wear sensor on/off, enable/disable auto standby, connection management (select which device the Px8 connects when powered on), etc. Once you havethe Px8 set up the way you want, the settings (including EQ) are stored on the Px8 themselves so you don't need to go into the app every time and you can just use your Spotify app to listen to your music. In fact, you don't even need the app installed on your source device. However, when you first pair the device, it will likely ask you to install and/or connect through the B&W app (you don't have to if you don't want to).
As for your question on Developer options, you don't need to mess with it for aptX. Codec selection will be automatic when you connect. I have both the Px7 S2 and Px8 and they both connect to my S22+ via aptX and my LG V60 and Creative BT-W4 (PC) via aptX adaptive automatically. No need to go into Developer options. Most recent Android phones, and certainly the S20 and S21 series, support LDAC but, to use it, both devices need to have LDAC. The Px8 does not support LDAC so with the S21 Ultra, your Px8 will default to aptX (Samsung phones generally do not support the higher aptX HD or aptX adaptive codecs unfortunately but aptX works just fine).