Find the WooCommerce catalog errors that cost sales

**Objective:** Audit the WooCommerce product catalog for data problems and report them grouped by rule. If `{category}` is given, only audit products in categories whose name contains it.

**Step 1: Pull the catalog**

* `woocommerce-get-product` with `max-records` 2000, and `categories.contains` = `{category}` when given.
* `woocommerce-get-product-variation` with `max-records` 5000. When `{category}` is given, keep only variations whose `product-id` is in the product set.
* Only when `{category}` is empty: `woocommerce-get-product-category`, `woocommerce-get-product-tag`, `woocommerce-get-product-attribute`, and for each attribute `woocommerce-get-product-attribute-term` with `product-attribute-id`.

**Step 2: Apply the rules**

Products and variations:

* **No SKU** on a published product or variation.
* **Duplicate SKU:** the same `sku` on two products, two variations, or a product and a variation.
* **No price:** `regular-price` empty or 0 on a published `simple` product or a published variation.
* **Bad sale price:** `sale-price` equal to or above `regular-price`.
* **Negative stock:** `stock-quantity` below 0.
* **Uncategorized:** `categories` empty or only "Uncategorized".
* **Variable with no variations:** a `variable` product with no variation rows.
* **Not published:** `draft`, `pending` or `private` products. List them without calling them wrong.

Taxonomy (whole store only):

* Categories with `number-of-products` 0.
* Tags and attribute terms with `count` 0.

**Step 3: Report**

1. A count per rule.
2. One section per rule, most harmful first (duplicate SKU, no price, bad sale price, negative stock, then the rest): up to 20 examples each with name, SKU, id and the problem, plus "and N more".
3. Suggested fixes. Point price and stock fixes at the update-product-by-sku prompt.

**Rules & Guidelines:**

* This prompt is read-only. Do not call any write tool: `woocommerce-add-order`, `woocommerce-update-order`, `woocommerce-add-order-note`, `woocommerce-send-order-details`, `woocommerce-add-refund`, `woocommerce-add-customer`, `woocommerce-update-customer`, `woocommerce-add-product`, `woocommerce-update-product`, `woocommerce-update-product-variation`, `woocommerce-add-coupon`, `woocommerce-update-coupon`.
* Pass `max-records` explicitly (500 unless stated otherwise). If a read returns exactly that many rows, say the result may be truncated and that totals are a lower bound.
* `grouped` and `external` products have no price of their own. Do not flag them under "No price".

**Validation:**

* If no products match `{category}`, list the closest category names from `woocommerce-get-product-category` with `name.contains` and stop.
* If the catalog is empty, say so and stop.