Should have been possible to choose that the alarm should also be notified on the phone.
Best answer by tkis
I have now found a solution (work around) on this issue. I think the problem is Android 9 Pie, and not the phone company, but maybe some phone companies fix the problem them self.
This is an app from Google Play called "Shouter". It is probably also other apps that will work, but this I have tested successfully.
This is an app that can read alerts to you (text to speech).
For me it is important that incoming SMS, and e-mail to selected accounts, notify me with a sound from the phone, even though I have Bluetooth headset enabled.
Install "Shouter" on your Android 9 Pie and choose which apps you want it to notify. Give the app all rights and enable it to boot automatically and run in the background.
What’s important is that under "Select audio output stream" select "Ringtone". This causes the notifications to come from both the phone and the headset.
Also go under "Device states" and deselect "Headphone Off". Then it will only alert you when you have connected your headset (I just tested with Bluetooth headset, not with wired).
Works perfectly for me, but I hope Google will fix the problem, because this probably uses some extra battery.
Since this app works, it means that someone can certainly create a small simple app for just this use. Where you can easily choose where the audio notification is playing. Hope someone does this unless Google itself can fix the problem.