Fix build_desktop_test for downstream runs

.github/workflows/build_desktop_test.yaml

@@ -31,6 +31,10 @@ on:
                 required: false
                 description: "Additional arguments to pass to playwright, for e.g. skipping specific tests"
 permissions: {}
+
+env:
+    REPO: ${{ github.action_repository }}
+
 jobs:
     test:
         name: Test ${{ inputs.project }}
@@ -38,7 +42,7 @@ jobs:
         steps:
             - uses: actions/checkout@de0fac2e4500dabe0009e67214ff5f5447ce83dd # v6
               with:
-                  repository: ${{ github.action_repository }}
+                  repository: ${{ env.REPO }}
                   persist-credentials: false
 
             - uses: pnpm/action-setup@fc06bc1257f339d1d5d8b3a19a8cae5388b55320 # v5