Make sure you have the latest version of the app.  Then see the instructions here:

https://support.sonos.com/en-us/article/add-your-music-library-to-sonos

Be sure you follow the links to share your music folder before proceeding to the add your music library in the Sonos app part. 

Thanks jgatie, but that I tried already few times. I can add my library there but it just does not show up under “My Sources”

Try logging out of your account on the app, and then log back in. 

Also, pardon what might be a Stupid Question, but in the new app (80.05.04 for iOS, in my case), is “My Sources” indeed the place where my music library would appear on the home screen? If so, does it appear there automatically after adding a music library (and I guess waiting for it to index), or is there some manual extra step to get the music library onto the home screen?

Actually, disregard my prior post. An hour later, my music library (on a Synology NAS, by the way) did show up under My Sources. Initially I could play songs from it. Then a few minutes later, I couldn’t: going into songs, or artists, or albums, etc. landed me in a screenful of grey blobs and no words loaded, and I got “Something went wrong. Try again.” Well, “trying again,” logging in and out, or killing the app and reopening, did not help. And the music library disappeared from the home screen. Then waiting 10 minutes and killing/reopening the app for perhaps the tenth time, it was back, and I could once again play music. So in short, it worked the way you’d expect from Sonos: performance is absolutely flaky, inconsistent, unreliable, undependable, transient, seemingly subject to the whimsy of demons and the phase of the moon.

Hi guys, went yesterday to my mum having the same system but using (old) Synologie nas. Configured the new app and guess what, it worked like a charme in one go. 
Back at home tried again and no luck whatever I try:

• remove the app and reinstall 
• deleted and re-added the nas share in the library
• tried as well from iPhone

I’m little reluctant to recreate the whole system as I don’t want to lose the function on my old iPad which still has the good old S2 app. 

Update: completely reinstalled everything including resetting all my Sonos devices. Adding them back worked almost fluently, but again no music library found. Checked on my old iPad, reconnected to the Sonos system and there the library showed up as supposed to be. So still in the dark with the new app. And worse thing, Sonos radio is not working anymore either @&#%!

My main suggestion is don’t let Sonos Support access your system. I lost access to my Synology NAS completely and had to get Synology support to help. Apparently the updates being worked on will resolve the music library issues. I am waiting with bated breath and very little confidence. I really hope that I am pleasantly surprised.

How are your Sonos devices and NAS connected to your network?

All are connected through Wifi. My old iPad with old S2 app recognizes everything, also the Sonos radio. On the Windows desktop app I can configure the music library with no issue either. It’s just the new app which can not find the library. Btw, v 80.06.03 did not bring solution too. 

This is, apparently, a “known issue”.  I had this today in a conversation with Sonos Support: -

“ “Thank you for reporting this to us. We are investigating the issue and do not currently have an ETA on when this will be fixed. I will log the case #********according to this issue so our team can look into this and come with a fix as soon as possible. You can also save a chat transcript after our session ends with this information. ”

So its official - Music Library no longer appears on the Home screen, at least for some of us - which is too many be far!