you have 2 problems in your Timecore setting,
- the input of the timecode for the Timecore should be internal, for now you have selected art-net.
- all the things you put in the show control are useless for your use, and you are now missing the button actions that would allow you to control the timecode with the front buttons of the Timecore.
To solve all those problems, Go in Vmanager and click on Factory default, once the Timecore had reboot, you can test the front buttons and the TImecode should be displayed on the Timecore.
Now, go in the web interface of the Timecore , go into the setting tab, and activate the Art-net output.
Now you should be able to get your timecode in Beyond.