The problem here is that HDMI carries audio. Period. When you plug in your monitor to your Mac via HDMI it's going to detect that there's an audio device attached. And, like you said, all you can do is mute, but mute has no effect because it doesn't remove the (audio) device; it just lowers the volume to zero.
The second problem is macOS. It assumes that whatever the latest audio device you plug in is the one you want to use. FreeBSD allows me to enumerate my audio devices then using
/etc/sysctl.conf tell it which one I want as my default. macOS has no provision for this.
(This is one of the things that drives me nuts about macOS - it assumes I did one thing, so I must want this other thing to happen. It's like an Apple engineer resurrected Clippy from a bit bucket somewhere). <\rant>
There are two ways to attack this:
Don't use HDMI. The specifications page for your monitor state that it has mDP (mini DisplayPort), HDMI, and DisplayPort inputs. Use either of the DisplayPort inputs instead (you'll get better performance and reliability anyway). I've found that most monitors don't carry the audio even though DP has the ability to do so. I'm guessing monitor manufacturers assume you want to use it as a computer display.
Use an HDMI audio extractor/de-enabler. This will allow you to intercept the audio signals in your HDMI cable and "remove" them for redirection elsewhere (i.e. SPDIF port on a home theater). If the end device doesn't present as an audio device as HDMI, there won't be anything to switch two.
Personally, I would go with the first option. It's the easiest and least complex way to achieve this - it's just a cable.