fix: add fallback for root-level static files in site-content handler

When an HTML page references static files (images, CSS, JS) via
relative URLs, the browser resolves them as root-level paths
(e.g. /image.jpg from page /site-name). Without a trailing slash
on the page URL, these resolve to /image.jpg instead of
/site-name/image.jpg.

The API's /site-content/{path} handler interprets the first path
segment as the site name, so /dule_yuan_15k.jpg was treated as a
site name lookup rather than a file within the dule-yuan site.

Added _find_static_file() fallback: when no site matches the first
path segment, search all site directories for a matching filename.
Only triggered for common static file extensions to avoid
ambiguous lookups.

home-apps/demo-service/service.py

@@ -127,6 +127,29 @@ def error_resp(status_code: int = 404) -> HTMLResponse:
     return resp
 
 
+# ── Static file fallback ─────────────────────────────
+def _find_static_file(path: str):
+    """Try to locate a static file (image, css, js, etc.) referenced
+    from a site's HTML as a root-relative URL (e.g. /image.jpg from page /site-name).
+    Searches all site directories for a matching filename.
+    Returns (site_name, sub_path) or None."""
+    filename = path.rsplit("/", 1)[-1]
+    if not filename or "." not in filename:
+        return None
+    ext = filename.rsplit(".", 1)[-1].lower()
+    if ext not in ("jpg", "jpeg", "png", "gif", "webp", "css", "js", "svg", "ico", "woff2", "pdf"):
+        return None
+    meta = _db.load_all()
+    for name in sorted(meta.get("sites", {}).keys()):
+        site_dir = DEMO_ROOT / name
+        if not site_dir.is_dir():
+            continue
+        candidate = site_dir / filename
+        if candidate.exists() and candidate.is_file():
+            return (name, filename)
+    return None
+
+
 # ─── File Helpers (NFS safe — no rename) ─────────────
 def sync_visibility(name: str):
     """Sync the on-disk index.html based on visibility mode."""
@@ -186,7 +209,17 @@ async def site_content(path: str = "", request: Request = None):
 
     info = _db.get(site_name)
     if not info:
-        return error_resp(404)
+        # ── Fallback: if the path doesn't match a site name, it might be
+        #    a static file (image, css, js) referenced from a site's HTML.
+        #    Try to find it in any site directory.
+        found = _find_static_file(path)
+        if found:
+            site_name, sub = found
+            info = _db.get(site_name)
+            if not info:
+                return error_resp(404)
+        else:
+            return error_resp(404)
 
     visibility = info["visibility"]
     user = check_auth(request)