chore(downloads): C1+C2 — drop dead target_ext; centralize path-traversal guard

- C1: remove downloads/formats.py target_ext() — defined but never called (the
  worker derives the real extension from the produced file's suffix).
- C2: the download-root containment+existence guard was copy-pasted 6× across the
  file-serving endpoints (routes/downloads.py ×3, routes/public.py ×3). Extract
  storage.safe_abs_path(root, rel) -> Path|None so this security-sensitive check
  lives in one place; behavior identical (same containment test + messages). The
  extraction also made `pathlib.Path` unused in both route modules (removed).

backend/app/downloads/formats.py

@@ -80,14 +80,6 @@ def format_sig(spec: dict) -> str:
     return hashlib.sha256(payload.encode()).hexdigest()[:24]
 
 
-def target_ext(spec: dict) -> str:
-    """Best-effort final extension for the produced file (also used to name the staging output)."""
-    s = normalize(spec)
-    if s["mode"] == "a":
-        return s["audio_format"] or "m4a"
-    return s["container"] or "mp4"
-
-
 def build_ydl_opts(
     spec: dict,
     outtmpl: str,

backend/app/downloads/storage.py

@@ -100,6 +100,17 @@ def abs_path(download_root: str, rel: str) -> Path:
     return Path(download_root) / rel
 
 
+def safe_abs_path(download_root: str, rel: str) -> Path | None:
+    """The resolved absolute path for `rel`, but ONLY if it stays inside DOWNLOAD_ROOT and exists on
+    disk — otherwise None. Centralizes the path-traversal + existence guard every file-serving endpoint
+    shares, so the containment check lives in exactly one place."""
+    root = Path(download_root).resolve()
+    path = abs_path(download_root, rel).resolve()
+    if root not in path.parents or not path.exists():
+        return None
+    return path
+
+
 def place_file(staging_file: Path, download_root: str, rel: str) -> None:
     """Move a completed staging file into its final location under DOWNLOAD_ROOT."""
     dest = abs_path(download_root, rel)