feat(downloads): M5 — Download Center frontend

- api.ts: download types + methods (profiles, enqueue, list/manage, file url, share,
  usage, index, admin storage/quota)
- format.ts: formatBytes / formatSpeed
- i18n: en/hu/de downloads.json (trilingual)
- Downloads nav module (Download icon, active-count badge, hidden for demo) placed after
  Messages; urlState page + App render + Header title
- DownloadButton: self-contained per-card/player affordance (demo-hidden, reflects the
  per-user download index: downloaded / in-queue), opens the preset dialog
- DownloadDialog: preset picker + optional display name -> enqueue + 'View' toast
- ProfileEditor: manage built-in + custom formats (full spec form incl. SponsorBlock)
- DownloadCenter: Queue / Library / Shared / (admin) System tabs, live progress via
  useLiveQuery, usage bar, pause/resume/cancel/delete, save-to-device, rename, share,
  admin storage dashboard + per-user quota editor
- wired DownloadButton into VideoCard + PlayerModal
- lib/nav.ts: decoupled navigator so the download toast can jump to the page

tsc + vite build clean. Verified in a headless authed browser: page + tabs render, Library
shows a real download with usage bar + actions, no console errors.

backend/app/routes/downloads.py

@@ -279,6 +279,29 @@ def my_usage(user: User = Depends(require_human), db: Session = Depends(get_db))
     return quota.usage(db, user.id)
 
 
+# Priority when a source has several jobs (e.g. a done one plus a fresh queued one).
+_INDEX_RANK = {"done": 4, "running": 3, "paused": 2, "queued": 1}
+
+
+@router.get("/index")
+def my_download_index(
+    user: User = Depends(require_human), db: Session = Depends(get_db)
+) -> dict:
+    """source_ref -> best active status, for the feed's per-card "downloaded / queued" badge.
+    Small + cheap so the feed can poll it without loading the full job list."""
+    rows = db.execute(
+        select(DownloadJob.source_ref, DownloadJob.status).where(
+            DownloadJob.user_id == user.id,
+            DownloadJob.status.in_(("queued", "running", "paused", "done")),
+        )
+    ).all()
+    out: dict[str, str] = {}
+    for ref, status in rows:
+        if _INDEX_RANK.get(status, 0) > _INDEX_RANK.get(out.get(ref, ""), 0):
+            out[ref] = status
+    return out
+
+
 @router.get("/shared")
 def shared_with_me(
     user: User = Depends(require_human), db: Session = Depends(get_db)