GHA: Fix nightly build notifications

.github/workflows/juce_private_build.yml

@@ -38,6 +38,7 @@ jobs:
           context: CI
           targetUrl: ${{ env.target_url }}
   build:
+    if: ${{ always() && (needs.setup.result == 'success' || needs.setup.result == 'skipped') }}
     needs: [setup]
     name: .
     # Not having the ability to do a dynamic 'uses' call is a real pain. To
@@ -78,7 +79,7 @@ jobs:
           description: ${{ env.result }}
           targetUrl: ${{ env.target_url }}
   notify:
-    if: ${{ always() && !contains(needs.*.result, 'cancelled') && inputs.nightly-targets == '[]' }}
+    if: ${{ always() && !contains(needs.*.result, 'cancelled') && !startsWith(inputs.triggerer, 'Nightly Build') }}
     needs: [setup, build, deploy, docs]
     name: Notify
     uses: juce-framework/JUCE-utils/.github/workflows/notify.yml@master

.github/workflows/juce_private_nightly_trigger.yml

@@ -8,7 +8,7 @@ env:
 jobs:
   juce-private-nightly-trigger:
     if: github.repository == 'juce-framework/JUCE-dev'
-    name: JUCE Push Trigger
+    name: JUCE Nightly Trigger
     runs-on: ubuntu-latest
     steps:
       - uses: actions/checkout@v4.2.2