Add FastAPI backend and React frontend subprojects

Backend:
- FastAPI app with 17 REST endpoints covering dashboard, monitoring,
  media index, file browser, and jobs
- Reuses existing clients/domain/services unchanged
- pydantic-settings config, dependency injection, CORS setup
- Auto-generated OpenAPI docs at /docs

Frontend:
- Vite + React + TypeScript SPA
- @tanstack/react-query for data fetching with polling
- ag-grid-react for media table and file browser
- recharts for monitoring charts
- Tailwind CSS styling
- 4 pages: Dashboard, Monitoring, Media, File Browser
- Typed API client matching all backend endpoints

Also:
- docs/MIGRATION_PLAN.md with full architecture plan
- Updated .gitignore for both subprojects
- Streamlit app preserved for now (can coexist)

backend/routers/files.py

@@ -0,0 +1,67 @@
+"""Files router — directory listing, ffprobe, stat, path resolution."""
+
+from __future__ import annotations
+
+import json
+from typing import Any
+
+from fastapi import APIRouter, Depends, Query, HTTPException
+
+from dependencies import get_ssh_client
+from clients.ssh import RemoteSSHClient
+from config import get_settings
+from path_utils import resolve_remote_media_path
+
+router = APIRouter(prefix="/api/files", tags=["files"])
+
+
+@router.get("/list")
+def list_directory(
+    path: str = Query(..., description="Remote directory path to list"),
+    ssh: RemoteSSHClient = Depends(get_ssh_client),
+) -> dict[str, Any]:
+    """List a remote directory."""
+    result = ssh.list_dir(path)
+    if result.exit_status != 0:
+        raise HTTPException(status_code=400, detail=result.stderr or result.stdout or "Failed to list directory")
+    entries = json.loads(result.stdout)
+    return {
+        "path": path,
+        "entries": entries,
+        "count": len(entries),
+    }
+
+
+@router.get("/ffprobe")
+def get_ffprobe(
+    path: str = Query(..., description="Remote file path to probe"),
+    ssh: RemoteSSHClient = Depends(get_ssh_client),
+) -> dict[str, Any]:
+    """Run ffprobe on a remote file and return parsed JSON."""
+    try:
+        data = ssh.ffprobe_json(path)
+    except RuntimeError as exc:
+        raise HTTPException(status_code=400, detail=str(exc))
+    return data
+
+
+@router.get("/stat")
+def get_stat(
+    path: str = Query(..., description="Remote path to stat"),
+    ssh: RemoteSSHClient = Depends(get_ssh_client),
+) -> dict[str, str]:
+    """Run stat on a remote path."""
+    result = ssh.stat_path(path)
+    if result.exit_status != 0:
+        raise HTTPException(status_code=400, detail=result.stderr or result.stdout or "stat failed")
+    return {"path": path, "output": result.stdout}
+
+
+@router.get("/resolve-path")
+def resolve_path(
+    path: str = Query(..., description="Jellyfin path to resolve to SSH path"),
+) -> dict[str, str]:
+    """Resolve a Jellyfin path to its SSH-visible equivalent."""
+    settings = get_settings()
+    resolved = resolve_remote_media_path(path, settings.media_root, settings.path_prefix)
+    return {"original": path, "resolved": resolved}