Make the job summary reflect whether a sync commit actually pushed

Both bots caught the same false report: the summarize step ran off the
initial drift flag, so the no-drift-after-rebuild exit still claimed a
commit landed on main. The commit step now records pushed=true/false in
its step output and the summary reads it.

Prepared with AI assistance (Claude Code), directed by @pbakaus.

Co-Authored-By: Claude Code <noreply@anthropic.com>

.github/workflows/sync-generated-output.yml

@@ -78,6 +78,7 @@ jobs:
           fi
 
       - name: Commit generated output
+        id: commit
         if: steps.drift.outputs.changed == 'true'
         run: |
           set -euo pipefail
@@ -97,6 +98,7 @@ jobs:
               # The race that beat us was another sync (or the rebuilt output
               # matches the new main); nothing left to push.
               echo "No generated output drift after rebuild (attempt $attempt); nothing to push."
+              echo "pushed=false" >> "$GITHUB_OUTPUT"
               exit 0
             fi
             git commit -m "Sync generated provider output"
@@ -104,6 +106,7 @@ jobs:
             git fetch origin main
             if git merge-base --is-ancestor origin/main HEAD && git push origin HEAD:main; then
               echo "Pushed generated output on attempt $attempt."
+              echo "pushed=true" >> "$GITHUB_OUTPUT"
               exit 0
             fi
 
@@ -125,4 +128,8 @@ jobs:
       - name: Summarize generated output commit
         if: steps.drift.outputs.changed == 'true'
         run: |
-          echo "Committed generated provider output directly to main." >> "$GITHUB_STEP_SUMMARY"
+          if [ "${{ steps.commit.outputs.pushed }}" = "true" ]; then
+            echo "Committed generated provider output directly to main." >> "$GITHUB_STEP_SUMMARY"
+          else
+            echo "Generated output drift resolved itself after a mid-run rebuild; nothing was pushed." >> "$GITHUB_STEP_SUMMARY"
+          fi