Since your Targus keypad connects by USB, not Bluetooth, we can rule out Bluetooth settings.
The behaviour you are seeing, where a number appears while you hold the key down but disappears when you release it, has been reported with some Targus numeric keypads when used with Excel for Mac.
On some Targus models, the Mac/PC setting can be important. (Microsoft Community)
A good first check is to open Notes and try the keypad there.
If the numbers stay on the screen after you release the keys, the keypad is working with macOS and the problem is likely specific to Excel.
If the same thing happens in Notes, check Num Lock if your keypad has it, and make sure Mouse Keys is turned off under System Settings >> Accessibility >> Pointer Control.
Apple notes that Mouse Keys can affect how a numeric keypad works. Apple: If a numeric keypad doesn’t work on Mac
If your Targus has a Mac/PC switch, set it to Mac, unplug the keypad, and plug it back in.
Some Targus models have this switch, but not all do.
As for the keyboard-type screen you saw when you first connected it, that is macOS's Keyboard Setup Assistant.
It is asking which physical keyboard layout you have, ANSI, ISO, or JIS.
It is not asking you to identify the keypad itself, so I would not change that setting again until we know which Targus model you have. Apple: Specify a keyboard type on Mac
The most useful thing you can give me now is the Targus model number printed on the underside of the keypad.
With that, we can check whether your particular model has a Mac/PC switch, specific Num Lock behaviour, or a known Excel compatibility issue.