Some applications such as Thunderbird do indeed seem to have their notifications include a sound, but this appears to be application-specific and the sound appears to be initiated from these applications separately from the notifications. For these applications it only appears that the sound and the notification are one in the same.
For the remaining applications (e.g. FireFox), my question is whether there is any way that the system can be configured so that notifications sent by applications will indeed play a sound?
Long story short, at the moment yes we live with no sound. In the future, this will change. GNOME folks are currently reworking the way notifications work, and the new API defaults to having sounds.
We can’t adjust the old API to play sounds by default, because apps rely on the fact that it doesn’t play sounds. For example: apps like Discord might choose to send notifications that are marked as slient, but then they play their own custom sound directly from the app, completely bypassing the notification system. If we update the old notification system to start playing sounds on silent notifications, apps that bypass the system like this will end up playing two sounds at once.
@adrianvovk Thank you much for the explanation. I had not seen an answer on this anywhere and it’s wonderful for the insight now.
Separately it looks like the notifications always play sounds on the Cinnamon DE, I’m not sure if Cinnamon uses a different API, or they use the same API but with some assumptions on their end.