Same issue here with multiple iOS 15.X phones while iOS 14.2 does work (instant when pluggin in an iBeacon). On iPhone 15 it only sometimes(!) work if you keep the app open/in the foreground and turn off the screen.
I've also tried to figure out if Apple changed policy and doesnt allow background iBeacon scanning any more (which would be very bad), but so far I did not find such release notes.
How unbelievable it might be, it seems like (background) beacon scanning is just completely broken for almost 1 year already. Back then Apple also didnt address the major geofence issues that happened back then. Fixing that geofence bug took months (it broken smart homes, security apps, door lock apps, etc, it was insane) and Apple also never took responsibility for it. No release note or bug update mentioned it.
I guess this Bluetooth iBeacon monitoring bug is very similair since it's part of the same monitoring logic with in the 'core location' framework.