Jetpack Search prevents partial text matches for WC Products

### Impacted plugin

Search

### Quick summary

When Jetpack Search is enabled, the "Product Search" block does not search for partial text matches.

### Steps to reproduce

Searching seems to be heavily cached and I recommend using a new private window for each search test.

1. Create a new WooCommerce store and import some products.
2. Access the Site Editor and add a "Product Search" block to the navigation, if it isn't there already.
3. In a private window, open the site and do a partial search for a product title. I used sample Woo products, tested with the "Beanie" product, and searched for "bean". You should see products returned.
4. Close all private windows to clear any caches and install JP/enable JP search.
5. Open a new private window and search for the same term in step 3. It should return no results.
6. In the same window, search for a full word in the product title from step 3 (eg "beanie"). It should return results.

### A clear and concise description of what you expected to happen.

Jetpack Search to support partial text match for products.

### What actually happened

Jetpack Search effectively prevents users from finding products unless they know the product title and search for a specific word in it.

### Impact

All

### Available workarounds?

Yes, easy to implement

### If the above answer is "Yes...", outline the workaround.

Toggle JP search off.

### Platform (Simple and/or Atomic)

Atomic, Self-hosted

### Logs or notes

_No response_

Reproduce the issue with a WooCommerce store, the Product Search block, and Jetpack Search enabled, following the private-window steps in the report. Compare partial-term and full-word searches, then trace the Jetpack Search integration for product queries; done means partial product-title searches return matching products without disabling Jetpack Search.

Written by the indexing model from the issue text.