I have a workaround.
Install Tasker, and two other plugins called Notification Listener and Blue Task. All are free.
Using Notification Listener, set up profiles for each type of notification you want to receive on your phone while connected to Blue Tooth. Under Tasks, use the Blue Task plugin to check if you're on Bluetooth (you can use If statements to filter specific devices) Set the task to "Play Music" and select the notification sound you want. Be sure to set media stream to Ringtone or Media (not notification) Finally, in System Settings under sound you set "Separate App Sound" to Tasker/Phone.
Note. Tasker and Notification Listener will run in the background in the notification bar. You can minimize those. If you don't mind getting duplicate notifications you can skip the BlueTask plugin altogether.
I'm sure there are other similar plugins that will work with this type of solution. Some lucky developer is gonna come up with an app that echoes notifications to the ringtone channel while connected to Bluetooth... And they'll clean house. Haha.
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