What to do If the native access library is not showing the Traktor software in the library after adding the serial code for the Traktor kontrol s4?
Looking at your dock: Traktor Pro 3 is already installed.
Which Traktor Kontrol S4? Mk1 or Mk2? These came with Traktor Pro S4 or Traktor Pro 2. As both versions aren't supported anymore (and therefore won't run on modern macOS versions) Native Access doesn't list them - even if their licence is tied to your NI account.
Is your S4 and the Traktor licence listed at "My products and serials" if you login to your NI account on the website? Maybe you have more than one NI account?