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Build a lightweight FastAPI search proxy using PostgreSQL with `pg_trgm` and `pgvector` extensions to serve product search queries for an ecommerce catalog.

1. DATA MODEL & SCHEMA:
- Create a `products` table with `id`, `title`, `description`, `sku`, `price`, `category_id`, `in_stock`, `attributes` (JSONB), and `embedding` (vector(1536)).
- Create gin index on `title` and `description` using `gin_trgm_ops`.
- Create a vector index (HNSW) on `embedding` using cosine distance.

2. API ENDPOINTS & SEARCH LOGIC:
- Implement `POST /products/index`: Accepts bulk JSON objects and updates/upserts rows into PostgreSQL. Automatically trigger an OpenAI embeddings call (`text-embedding-3-small`) to generate vectors for `title` + `description`.
- Implement `GET /search`: Accepts `q` (string), `filter_by` (category, price range, stock status), `sort_by` (price, relevance), `page`, and `per_page`.
- Query logic: If `q` is short (<3 chars), perform exact prefix matching. If `q` is longer, execute a hybrid search combining trigram similarity (`similarity(title, q)`) and vector distance (`1 - (embedding <=> query_vector)`). Combine scores with configurable weights (e.g., 0.6 keyword, 0.4 vector).

3. FACETING & AUTOCOMPLETE:
- Return faceted counts in the search response for `category_id` and price ranges using bucket queries.
- Implement `GET /autocomplete`: Fast, low-latency prefix search returning top 5 matching product titles and category names using trigram index.

4. FAILURE MODES & HARDENING:
- Gracefully fall back to keyword-only search if OpenAI API vector generation times out (>500ms).
- Sanitize all text input against SQL injection.
- Cache autocomplete queries in Redis with a 5-minute TTL.

5. OUT OF SCOPE:
- Do not build custom C++ binary or C++ memory structures.
- Do not build complex distributed multi-node replication; rely on standard PostgreSQL replication.

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