Are you saying the menu key has never worked before?
Are you sure you have the correct keyboard layout?
For 20.04 use system settings. For 22.04 same as below but use budgie control center
Choose System Settings.Click Keyboard Layout. The Keyboard Layout window opens. Click the plus (+) sign in the bottom-left corner to open the available keyboard layouts.
There is no icon there which is the strangest thing. How do I get the menu to come back? I have updated and rebooted but I have not tried creating a new user yet.
There is also not a hardware issue because the super key works for everything except opening the menu.
I suspect that somehow the menu process got killed or something like that. How can I turn it on again?