There are two valid ways to enable the global Hotkey support for switching between your Rooms (which are assigned to Spaces) using CurrentKey Stats. (Where you can quickly jump between them using keyboard shortcuts).
The first way requires giving the app Accessibility permissions in macOS' System Settings. This is a great option, but I have run into what seems like a macOS bug — present in the latest public beta of Sequoia and affecting computers with multiple User accounts — that prevented me from adding the app to the Accessibility list.
The "second" way involves using the AppleScript functionality and a third-party app, like QuickSilver, to tell CurrentKey which Room/Space to go to, programmatically.
The first way to enable it is the one that's described in the app itself: You head to your Mac's System Settings, click on "Privacy & Security", then click on "Accessibility", and then add CurrentKey Stats to the list of apps that can "control your computer".
The second way to enable global hotkeys I find superior: because: 1.) it does not require that you grant CurrentKey Stats any permissions, and 2.) it is less dependent on macOS to … not be finicky … during setup.
Enable global Hotkeys support via AppleScript
The second way to enable hotkeys:
You can use an app like QuickSilver to listen for Hotkeys and set an AppleScript to execute the command. (Alfred may work too for this but I personally use QuickSilver.)
First, go to the Background Services panel and enable in-bound AppleScript support. The following check-mark needs to be checked for this AppleScript feature to work. This is found in CurrentKey Stats -> Settings -> Background Services:
Next, open up the Apple app called "Script Editor" and create an AppleScript that can be as simple as:
tell application "CurrentKey Stats" to gotoroom called "MyWork"
Notice in QuickSilver I set the hotkey "trigger" to "Control(^) plus Option plus M", and the command to the AppleScript itself. And Voila! Whenever the hotkeys are pressed, the script runs, and it moves me to the MyWork room instantly.
If you already set up hotkeys using AppleScript, that's a great reason to check out the other cool things you can do with CurrentKey and AppleScript. And here are a few blog posts exploring some of the ideas in detail.