Is it possible to have workout audio prompts only on headphones and not on smartphone?

I get that too! I normally run with bone conduction headphones, but I do parkrun without headphones.

It's more an app question.

https://forums.garmin.com/apps-software/mobile-apps-web/f/garmin-connect-mobile-andriod

https://forums.garmin.com/apps-software/mobile-apps-web/f/garmin-connect-mobile-ios

With my FR955 and Jabra bluetooth headset it is no problem. Always have the audio prompt in my ear. You should look somewhere in the bluetooth settings. Is your earphone connected to the phone, or to the watch? And do you play music? From phone or watch?

EDIT: I did not read your question well. I understand you want your phone to be silent when you are NOT running with your earphones. I am afraid you just have to mute your phone then. There is no autoselect or something. Audioprompts are on, or off, regardless any headphone connection.

I think this is by design. The only way I mute that on my Phone is --- guess --- mute phone sound completely. Tested. It works.

If you do not like to hear workout announcements than you most likely do not listen music or audiobook thru phone speakers.

Yes, I mute the phone too, but it is a move that could be avoided by adding a setting on the watch.

I don't listen music or audio books through phone, I'm old

Fully agree.

Last thing we can do is to suggest this via www.garmin.com/.../