How do you know that the drone is even connected to your neighbours WiFi??
It might just be a bog standard radio controlled drone. Or a camera drone with no streaming capabilities.
I’m not going to go into any specifics, but with Kali, you can put your WiFi card into monitor mode (if your card supports monitor mode) and can see all networks in range of your WiFi card.
Once you’ve identified which network your neighbour is using, you can monitor that network and see which devices are connected to the network and may even be able to identify what type of devices they are, what OS etc.
If you’re only monitoring local network activity, you’re probably ok from a legal standpoint.
But if you attempt to access, or attack your neighbours network, or connected devices without their permission - you’re breaking the law. So be extremely careful with that.
If their late night drone flights are a nuisance, perhaps consider talking to your neighbour about them and try asking them to fly their drone at more sociable hours?!
And if they own a camera drone and you feel that your privacy is being invaded - perhaps try asking them not to fly too close to your property. If they decide to be unreasonable about it - have a word with your local police to see if there anything they can do?!