agent: stop the launcher claiming it cannot push when it can

The `loose` footer announced "cannot push -- no git credentials are mounted"
unconditionally. It was written before the credential mount existed and then
went stale, so with credentials correctly mounted it told the operator their
work would be lost -- the exact failure the mount was added to prevent.

It now reports what is actually true, and keeps the real warning for the case
where the file genuinely is missing.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

docker/agent/sylph-agent

@@ -229,8 +229,19 @@ case "${1:-}" in
     echo "      ./sylph-agent attach      chat with it locally (Ctrl-P Ctrl-Q to leave it running)"
     echo "      ./sylph-agent stop        stop it"
     echo
-    echo "    It commits to auto/* branches and cannot push — no git credentials"
-    echo "    are mounted, so review its work with: git -C '$PROJECT/Syplheed-Reborn' log --oneline auto/..."
+    # Report what is actually true. This line used to claim unconditionally that
+    # the agent could not push, which was written before credentials were
+    # supported and then went stale — telling the operator their work was at risk
+    # when it was not, which is the exact failure the credential mount fixes.
+    if [ -f "${SYLPH_GIT_CREDENTIALS:-$HOME/.sylph-git-credentials}" ]; then
+      echo "    It commits to auto/* branches and publishes them with push-work,"
+      echo "    which refuses any other branch and never force-pushes. Review with:"
+      echo "      git -C '$PROJECT/Syplheed-Reborn' fetch origin && git log --oneline origin/auto/..."
+    else
+      echo "    It commits to auto/* branches and CANNOT PUSH — no git credentials"
+      echo "    are mounted, so its work dies with the container. Review it with:"
+      echo "      git -C '$PROJECT/Syplheed-Reborn' log --oneline auto/..."
+    fi
     ;;
 
   logs)   shift; exec docker logs "$@" "$NAME" ;;