if i understand you correctly, that's muting conversations on a one-at-a-time basis, which is not the same as being able to globally disable notifications from the app
You can disable those too, click the "Profile" icon (the one with the silhouette) at the main screen, third menu option after user name and phone number is notifications. Globally.
on android at least, you can always globally disable notifications from an app: long press on a notification, tap the little i in a circle that appears, and there should be an "allow notifications" box you can un-check.
Well...you have incremental time options, or you can set it to "Until I turn it back on". Only globally has a limit to turn off EVERYTHING for 24 hours. Otherwise, you can disable wholesale the sound and popup notification with no max time. I'm no FB support person, just a heavy user of the App.