Hello seanmh72,
Thank you for using Apple Support Communities! I understand that you're hearing system and notification sounds after turning the volume down on your iPhone 11 Pro. I would be happy to help provide more information about this behavior.
Are you seeing the line through your speaker when viewing the audio card in the Control Center on your iPhone? The "Control audio" section in the resource below shows what I'm referring to:
Use and customize Control Center on your iPhone, iPad, and iPod touch - Apple Support
If that's where the volume shows as muted, then this will mute only speaker sounds for music, movies, and other media. If that's what's happening, you are correct that you would want to put your iPhone on Ring/Silent mode, or turn down the ringer and alert volumes to mute the system and notification sounds instead:
Take care!