I downloaded your three macros from above, and they work fine here, too.
If you want to launch the master macro (Toggle Internet) from BTT, then just use the same method you are already using for launching the two sub macros from the master macro: via AppleScript.
You find the the premade AppleScript to launch your master macro in the “Or by AppleScript” popup:
Then you paste that script to BTT here:
…and set the BTT trigger you want.
BTW, to launch the sub macros from your master macro, you can also make use of the Execute Macro action:
It is made for such cases, so no need to use an AppleScript action here.