To use it in Logic, you need to insert the Plugin version into an audio track (The same as any other Plugin). I’m copying a troubleshooting guide in case you can’t find it inside Logic:
Regarding the Cali, since you already installed iLok License Manager, you just need to run the Standalone and click “Try” when the activation screen appears.
First, you need to create a new audio track in Logic and then insert the Plug-In version on the track at the Audio FX slot (you will find it at Audio Units > Neural DSP). Just click on “Audio FX” and look for the Plug-In (be sure to select AUDIO TRACK instead of instrument track).
After that, you will need to enable monitoring to hear the signal: