Turn iPad bluetooth off remotely? Switch Control?

I have a set of bluetooth headphones than can dual connect to both my iPad and iPhone simultaneously (Jabra 75t Elite Active). Most of the time, I think I like this functionality, but sometimes it’s annoying because I leave my iPad upstairs, and when I’m connected downstairs with my iPhone it will frequently announce that the headphones connect and unconnected with the iPad. In these times, I would like to be able (ideally) to manually turn off Bluetooth on my iPad remotely from my iPhone.

Is there a way to do this? I was trying to investigate the Switch Control functionality, but couldn’t figure it out. Any suggested solutions would be great (yes, I know it would be nice if I remembered to turn bluetooth off my iPad before going downstairs, but I haven’t formed that habit yet!)

on iOS 14 you can set up a shortcut that turns off your bluetooth when you receive an email / text with a certain text in the subject / iMessage, like “turn off bluetooth”

If you only enable that on your iPad you should be ok.

Only thing I’m not sure about is whether your iPad refreshes your email often enough, so iMessage is probably better. Just iMessage yourself.