With my drone pilot hat on now..
Lots of bad advice given here, ill clear some of these 1st.
"Air rifles are not firearms" - They very much are! You are very likely to have unplanned visitors VERY quickly! - they wont be friendly or approachable.
"but if she can't locate the owner who the hell is going to prosecute for criminal damage? And she's got mitigating circumstances." - no mitigating circumstances at all, annoyance is rubbish and remember even a sub 250g drone has a 4k camera and this also sends a video feed back to the controller/phone which can be checked later to see you brandishing you weapon, even picking up the drone and taking it if you were foolish enough.
Drones are classed as aircraft and shooting / throwing rocks etc would see you in court as if youd done that to a plane or glider.
Drones "should" always be flown in clear line of site, so the operator of a sub250g drone should be within say 100m and have an unrestricted view of it - this might help you track them down.
Thats the law, but as we know, no all humans dont like to follow laws and stretch boundries think 155mph bmw doing 100 on the motorway, most popular the DJi Mini2/3 will happily fly over 1km away in the ek/eu.
The operator is most likely not even remotely interested and hasnt noticed you. If you found them and asked them/told them your concerns they would probably be more than happy to avoid you and even show you what they are actualy doing.