Hi @jonatha
Welcome to the Sonos Community!
I am sorry to hear of this issue you are having with being unable to play Music Library Albums on your Sonos system from your iOS device.
My colleague (I do not have an iOS device) was unable to recreate this issue in his own testing - he was able to play from Recently Played and Favourites.
I did forward him the diagnostic from your case and he did spot that you have four separate folders shared, and wonders if you might get better results if you removed them all and replaced them with a single share to the parent directory of those four shares instead.
If this does not help, please record a screen-capture video of the issue you are having and post it here (you will likely need to post to YouTube and mark it as a public video, or upload to Google Drive (or similar), then post a link). Please also submit a support diagnostic, but do not share the number given - just let me know here when you have done so and we will take a closer look for you.
Incidentally, I feel it is misrepresentative to say “considering Sonos support didn't go beyond asking me to restart the phone and reinstall the app” - the agent would have gone further given a chance.
I hope this helps.