Hi, KentOhana.
Thank you for posting in the Apple Support Communities.
We understand that you’re connecting an LG and HP external monitor to your Mac mini, but you’re not able to select them as your sound output option. Have you had a chance to figure out why the monitor isn’t accepting your sound settings?
Looking at the tech specs for a Mac mini, it looks like there is HDMI 2.0 port support for multichannel audio output. You can connect one external monitor via HDMI and one via Thunderbolt, but only the one connected via HDMI will support audio with an HDMI 2.0 or later cable. If you're not able to select it for your sound output options, and you have it connected with a good HDMI cable, you might check to see if there are any drivers or other firmware for the monitor that needs to be installed on your Mac mini.
These are the tech specs for the Mac mini (2018) to confirm the options:
Mac mini (2018) - Technical Specifications
Regarding using your Google mini speaker, you may be able to connect it to your Mac mini via Bluetooth using the Google Home app on your phone or the Bluetooth settings on your Mac.
Play music on your speaker or display using Bluetooth - Google Nest Help
Best Regards!
