On the Enduro 3, which lacks the Fenix 8´s speaker, disabling the beeps completely is not possible. You can enable and disable the sounds for buttons systemwide and the vibrations system wide, but cannot do the same the sounds system wide. You can enable or disable sounds for smart notifications, sure, but not for fitness notifications like move alerts and system alerts like phone disconnect alert, even according to the official manual.(1)
Quite a strange decision. Now, I have disabled most of system and fitness notifications completely and thinking about going back to my older forerunner. Not being able to disable all sounds and beeps is not only annoying for me as a teacher in front of classes, but also distracting during their lessons and a bad example as I forbid using/reacting to phones and wearables in the classroom.