Is there a way to natively add a system microphone control icon next to the system volume control icon in the Gnome top bar?
Also, why is this control not there by default as system volume is?
SnapOverflow
You can use the extension Sound Input & Output Device Chooser which will modify the icon in the top bar, allowing you to change the input levels of the microphone, and to choose what device is active.
It's another extension, but I can definitely recommend Nothing to Say. Not only does it give very visual feedback on whether your microphone is active, it also gives you a global shortcut key to mute/unmute yourself.