Also affects version 1.16.1 - just noticed this today while playing that version.
Also confirming, still present in 1.16.1.
I might add that this effect is also created when you push the mouse button down, hearing a click and entering a menu, move the mouse to be on top of a slider, and then releasing. You still get an extra click. A nice place to demonstrate this is from the Minecraft title screen: move the mouse over the Options button, press down on Left Click, continue to hold down the button while moving the mouse up to the FOV slider, then release. Extra click sound.
EDIT: Strangely, moving the mouse to be over a slider does not produce the extra sound when entering the Video Settings menu, but does work in Options, Music & Sounds, Controls, Chat Settings, and Accessibility Settings.
This issue was "fixed", but it was fixed quite poorly, resulting in the equip sound being played in numerous situations where it shouldn't be played.
Detailed in this video: https://youtu.be/VFv7incNxdQ