This is a misunderstanding or a bug in the app. Bluetooth and GPS on a technological level have nothing in common.
However Bluetooth can also be used for calculating your location e.g. by special beacons that transmit their coordinates via Bluetooth. If you are within reception range of such beacon(s) the phone or an app would be able to calculate your position with a precision of 100 meters or less. For that reason in Android before version 12, an app had to request fine location permissions for Bluetooth scanning.
Since Android 12 there is an own permission and you can declare that you never use it for location. Then such location declaring beacons will be filtered from the Bluetooth scan result.
In your case you should check Android settings if you have disabled location services for the whole device (may be because you thought that this will never be needed). Without location services requesting the location permissions may fail.
Only on devices that neither have GPS nor cellular nor Wifi you may run into problems if the location services has been removed by vendor (because someone thought that without GPS/cellular/Wifi location services are not needed).