I have developed a few apps using bluetooth and something i keep forgetting is the capabilities in xcode.
I have mostly done it in flutter.
When opening your target "Runner" go to signing and capabilities.
Click on the "+ capabilities" and look for "background execution modes"
When using BLE go select the bluetooth le... checkbox.
clean build folder and restart xcode or the ide you are using and go rebuild ios. REBUILD EVERYTHING.
Assuming, you also have the correct permissions in the info.plist.
additionally bluetooth requires location too so select accordingly.