By using your second ethernet link, it will be expecting a DHCP Server, a DNS server, and a Router on that 2nd network, which you dont have. You will also need to configure the Mac on how to use those two networks. There are so many combinations here, its too much to explain, but as has already been said, I think you are overthinking, and doubt very much you will notice any quality difference, so suggest just plus the Muso into your normal network. Then you have two options
either install Asset or Minimserver on your Mac to share out music via UPnP
and/or if your 3.5mm output supports toslink, then as @NogBadTheBad suggested, get a cable to link the optical output of the Mac to the Muso, after which all Mac output will divert to the Muso
The 500-series Naim systems are the most expensive ones below the Statement.
The comment is meant in the sense, that people will go to various lengths to optimize the output from such a “500 system”, because it’s really great and costs a small fortune (for most people).
The Muso is several classes below that, so the comment means, not to over-engineer the connectivity in relation to the audio-capabilities of the Muso.
Since I sense some confusion in this thread, I’ll put another comment below. (Just bear with me, it’ll take a few minutes.)
I think some of the confusion comes from the fact, that there’s (at least) 2 very different approaches, how audio is handled in Muso, Mac, and most (home) IT environments today. (And that blend over to each other. All of the below is simplified, for some brevity.)
Direct audio connections, usually direct links (often cables, possibly radio) between physical devices and handled as “audio output options” in the sending device (like in the audio output settings on a Mac, Windows or Linux PC). Usually handled as “input devices” on the receiving side. Usually uni-directional. (Hence the output/send → receive/input terminology.)
Examples:
Analogue audio links, usually via (copper) cables using connectors like classical cinch, jacks, DIN-plugs, … - the stuff we used for decades to interconnect audio devices, headphones, and the like. The Muso has 1 such input, to all I know. All the flexibility and compatibility of decades of audio devices using this, all the challenge to get analogue signals across wires “without changes”.
Digital audio links, via optical or electrical cables, using the SPDIF, BNC, or other plugs. The Muso has 1 optical-in, to all I know. Can get “lossless data” from A to B, possibly challenges with timing, etc.
(EDIT:) HDMI-ARC is another variant of a direct digital connection. However, only TVs and some A/V receivers have HDMI-(e)ARC capability (it’s the same plug, but another protocol than transmitting straight video across). You will not find any Mac, PC or the like with an (e)ARC output. So this option is useless for connecting Muso to Mac. (Unless you put a TV or receiver in between those two.)
The Muso only has a HDMI-ARC input, nothing which works with standard HDMI.
(You could consider Bluetooth connections as one such option. That’s due to specialized profiles for Bluetooth that emulate various use cases, in this case “audio channel”. Challenge here is the low bitrate, the non-lossless transmit (at least for Apple), and others.)
(EDIT2:) Ethernet will never show as such a connection. It’s built for something completely different. (For the options below.)
(IP) Network based ways to transmit music via networked devices. At home, this will usually be Ethernet or WiFi (ignoring e.g. mobile cell networks, which don’t help much within your home). Since the IP networks are fast, bi-directional, and on application fully flexible/programmable, they offer up plenty of different protocols and also “models”, how music can be transferred and played. Relevant in this discussion here:
UPnP / DLNA: a model, where 1 entity acts as the “source/storage” of the music, 1 entity is the “renderer/playback” and a 3rd entity is the “controller”, binding the 2 others. The controller can be in either of the 2 others, or separate. This is a bit more following the client/server/“files to send” thinking of IT systems, than classical audio thinking.
The Muso has a renderer built-in, and the Naim app can act as controller (kind of). So, if you have music on a PC, NAS, Mac, … you can run a “server” there, and access the music from the Muso via network. On a Mac, you will need a 3rd party server application to run to use this.
Airplay, as an in-built “casting/streaming” service, which emulates again more an audio connection from a source to a destination. Plus it uses a “control channel”, where either side can tell the other to start/stop/change volume, and a few tricks more. It’s an Apple thing (Google has e.g. Chromecast), and hence well built into macOS (and i(Pad)OS). Up to the point, that in latest versions any Mac, iPhone, etc. can be either source or destination. For audio and/or video. So, from the perspective, it seems a bit like an audio device/output, like those from the first list of options.
However, the connectivity between source and destination uses any existing local IP network in place. It’s not intended to rely on a point-to-point connection. Therefore people tell you, to just connect both Mac and Muso to your home network (usually the internet router, possibly using more switches, WiFi, WiFI mesh networs, or whatever you have at home).
Lastly, while it’s called “Airplay” it does totally not matter (from functionality), if you use WiFi or Ethernet for any of the involved devices. So, if you hook up both Muso and Mac via Ethernet, you’ll have a complete cable-bound connection, irrespective of “Air” being part of the protocol name.
Streaming services - in case you’d receive music on the Muso directly from the internet, via Tidal, Qobuz, or Spotify. (Apple and Amazon Music not supported.)
So, the easiest ways out for you likely are:
Connect Muso to your home network. Use WiFi if that works fine, use Ethernet, if it’s not too much hassle to put in place and you prefer the reliability of the cabled connection.
Use Airplay from Mac to Muso, if that’s fine with you. Control music from the Mac (or your iPhone via the “Remote” app). You can play easily anything in Music (former iTunes), since it’s very Airplay aware. But you can play anything on the Mac that can feed into the (virtual) Airplay output “devices”, including the whole Mac default output. (Via general audio settings.)
Look into a UPnP server software, if you want to control playback via the Muso, the Naim app, or something else.
Anything else (like an optical SPDIF direct link, …) will need additional hardware (like cables, converters, a dedicated NAS to store/serve the music, …) or not-so-convenient setups.
You possibly could connect the Muso to the Mac as you did, and configure the Mac to relay traffic to/from the Muso towards your LAN/internet connection and make it work. If you are into IT/IP networking, and like to fiddle around with such stuff. But it’s not intended for this, will need non-standard configuration and will give you no extra benefit, except for a more complicated setup.
UPnP can work with high-resolution losslessly encoded music.
Airplay can work with lossless audio (about up to CD quality), but still does not support higher resolutions. In iPhones, especially when playing from Apple Music service, it will actually use lossy AAC codec.
So the choice between those 2 can also depend on the music in your library - whether it’s AAC, lossless-CD, or higher resolution files.
That’s where the “it’s not a 500 system” comment comes from - likely Airplay is “good enough” for a Muso either way.