Did you manage to resolve this? I'm encountering the same error when I upload my app to Testflight.
This feature (waking up the app when something happen over BLE) is not supported in watchOS.
Communicating over BLE when the app is in the background and not suspended works even without this background mode
The 'com.apple.developer.bluetooth-central-background' entitlement is required for apps to use CoreBluetooth background capabilities on the watch.
This is a special entitlement given out very selectively, and currently it is only available to developers with watchOS apps communicating with Continuous Glucose Monitoring devices.
We currently have no timeline we can share, about when this might be expanded to other applications.