Please check /Applications/Utilities/Activity Monitor.app. You should find a process named HoudahSpotHelper, but I guess you won't. The HoudahSpotHelper is in charge of both the menu item and the keyboard shortcut.
If you can't find the HoudahSpotHelper it probably failed to start. That is most likely caused by a failure of macOS Gatekeeper. When you download an application, it is flagged as "quarantined". The first time you run it, the Finder will ask if that is OK. When you agree, it will remove quarantine flag so you don't get asked again. The Finder/Gatekeeper should remove the flag from both the main application as well as helper tools included within. Sometimes it forgets. Then the helper cannot launch. Since it is meant to launch in the background, you won't be asked to agree to launching. It will just fail.
1. Open /Applications/Utilities/Terminal.app
2. Paste in the following: "xattr -r -d "com.apple.quarantine" " (without the enclosing quotes, but with the trailing space)
3. Drag HoudahSpot.app from the Finder to the Terminal window. This will append its path to the command. You will probably see:
xattr -r -d "com.apple.quarantine" /Application/HoudahSpot.app
4. Press Return/Enter
This will remove the quarantine flag.
Return to HoudahSpot > Preferences > Shortcuts and toggle the Helper off and back on. It should launch, and supply the icon and keyboard shortcuts.
Houdah Software s.à r.l.