The Sonos app doesn't properly show the song that's playing when Sonos ace is wired

Not sure I understand. The controller app is merely a remote control, an app to see what the player on the speakers is playing. The Sonos controller doesn’t ‘play’ any music. 
 

The Ace doesn’t connect as a ‘room’ in the Sonos ecosystem, so it doesn’t ‘play’ music. It acts as a Bluetooth receiver for other apps (technically, the OS) to connect to and play music. Or uses USB-C to accept that music input, but it isn’t ‘playing’ music like a Sonos speaker. So other than software updates, there is no music connection between the Ace and the Sonos controller. 

I'll show you the images. I have the headphones connected by cable. The song it shows in the playback does not match the one I am listening to. Show the last one I heard by Bluetooth (pic2)
If nothing has previously been played by Bluetooth, it shows unknown content (pic1)

It's a screenshot of the Sonos app while I play music by USBC cable on my iPhone

What player are you using to feed the USB-C connection?

Apple Music app

Not sure I understand why, but as I comprehend the pathway, the Apple Music app is sending its data to the Sonos Ace. The Ace would be receiving it, and then reporting back to the Sonos controller what is being sent to it. I’d guess one of those connections is not working properly. 

Have you called. Sonos Support to discuss it?

When you speak directly to the Support staff, they have tools at their disposal that will allow them to give you advice specific to your network and Sonos system

I really think that the Sonos app is not able to get the playback information through the USBc.

It is not useful or nice to show the title of another song. The app should be modified so that while Sonos Ace is connected by cable only the playback controls are shown and omit reference to the title song

Possible, I don’t know. But the number of moderators on this board are extremely few, however, if you make it a feature request they’d likely pass it on. If you think it’s a bug, then you’re more likely to have the information passed on by calling in than posting here. 

If the Ace is wired via USB-C you aren’t doing an Audio Swap with a Sonos sound bar. Wiring the Ace you should be getting your audio from music streamed or stored on your device via the native streaming application such as Apple Music, Spotify or similar. There is where you will find the song that you are listening to and not in the Sonos app.

For example, I have AppleTV which also supports Apple Music. I can access my Apple Music collection via AppleTV that is connected to my LG TV which is connected to my Arc Ultra. I can perform an Audio Swap and listen to the music through my Ace. However, the song playing will still not be visible in the Sonos app.

As you can see in the screenshots, with Sonos ACE connected via cable, the Sonos app shows playback control, allows you to vary the volume, pause and change songs. But it doesn't show the correct reproduction. I don't know if it's an app failure or a limitation, the fact is that it's quite ugly or annoying.