Set default speaker of Google Nest Mini via Home Assistant

I’m using the Google Cast integration to cast music, tts and sounds to my speakers.
In the living room I have a Nest Mini and a non-smart Soundbar+Subwoofer which sounds way better than the tiny Nest Mini Speaker.
The Nest Mini has the option of changing the “default speaker” to the soundbar (via Bluetooth) which works fine but must be done manually through the app or via voice command (“hey google, connect bluetooth”).

Is there any way to easily set this default speaker setting via Home Assistant?

I need this exact thing! Real pain having to keep going into Google Home app.

I found a solution which works fine for me: Assistant Relay Alternative - #20 by brintal

The only downside is that the assistant vocally announces that it is now connecting to the Bluetooth device. But that doesn’t really bother me.

@brintal , hi

how can I do that?
I have both configure Google Assistant SDK and Google Assistant integrations on my HA, but I cannot figure out how create Helpers on HA and Actions like “Connect blabla speaker to bluetooth” on Google assistant routine, any advice?