First, the full screen output is really designed for preview, the quality might not be very good.

Now, for the audio, you’ll need to route that separately in your audio output settings.
You could set the master Output to HDMI (Usually called Nvidia...), or you could route it to HDMI through the buses.

Fullscreen outputs can indeed be used for external encoders, and are certainly not limited to preview.

But Vince is right regarding setting up audio (Settings/Audio Outputs) using Master and Buses to route audio to the PC's monitor(s).

Note a couple of things.

First, display resolutions and frame rate set in Windows for the monitors are handshaked with EDI info from the monitor, so if you set the resolution in Windows to for example 1280x720 the encoder (e.g. LiveU) might force it to 1920x1080. Typically no big deal.

Second, setting up resolutions in Windows and audio output in vMix with one monitor (e.g. a Dell) will need to be changed if you change to another monitor (e.g. a Sharp projector at a venue). vMix remembers the Dell, so you have to change audio output to the Sharp. And of course make sure Windows display settings are correct. Even if you use a LiveU Solo both when testing/prepping and live on location, things may change if other monitors are used. Ususally no problem, just so that you are aware of the issues.

Good luck!

If I may add my 2 cents on Fullscreen output, from what I have seen using it for my preview monitors, the quality and frame rate consistency is far for optimal compared to using an external output via thunderbolt to an IO4K or a Blackmagic/Covid card.