Mac Mini Sound Output won't play tunes from bluetooth connected ipad

I'm not great at connecting things but I just realized I can play my ipad via bluetooth to a small bluetooth speaker in my bedroom, which made me want to connect the ipad via bluetooth to my Mac Mini desktop (with monitor (a TV) and speakers) in my living room.

I got the Mac Mini to see the iPad and vice-versa, so they are paired and show as connected, but I can't get the music from my ipad to come out of the computer speakers.

I went to Sound/Output but it only shows the TV and "Headphone Port" which is how I have my speakers hooked up. The speakers work when I play something on the computer.

So how do I get the Sound Output to play bluetooth? I've tried pairing and unpairing...

What am I missing?

Thanks in advance.