Apple - Spotlight shortcut (cmd+space) no longer working
On MacOS Catalina, the issue may be caused by the
SystemUIServer process hanging.
You can restart it by launching the command
I found out that BetterTouchTool was running in the background and somehow had cmd-space assigned as a shortcut with no action (I definitely do not remember doing this). For others with this issue, I would advise carefully considering apps running in the background when checking for conflicts.
Have you checked the system preferences -> Keyboards -> Shortcuts -> Spotlight and made sure it was checked?
Does it work in safemode? What about other user accounts?
If not then you may need to reinstall MacOS from recovery mode.