fix push-to-action: use CLI direct invocation for token acquisition

the inline `node -e` + `TOKEN=$(...)` approach broke because
`core.getIDToken()` in @actions/core writes `::debug::` and
`::add-mask::` to stdout, polluting the captured value.

`node cli.ts gha token` uses `core.setOutput()` which writes to
the $GITHUB_OUTPUT file instead of stdout.

Made-with: Cursor

tsconfig.json

@@ -20,5 +20,6 @@
     "stripInternal": true,
     "moduleDetection": "force",
     "useUnknownInCatchVariables": true
-  }
+  },
+  "exclude": []
 }