[Backport to release/11.1] Include product brands in term recounts - #67656

This PR is a cherry-pick of #67630 to release/11.1.

Original PR Description

Submission Review Guidelines:

• I have followed the WooCommerce Contributing Guidelines and the WordPress Coding Standards.
• I have checked to ensure there aren't other open Pull Requests for the same update/change.
• I have reviewed my code for security best practices.
• Following the above guidelines will result in quick merges and clear and detailed feedback when appropriate.

Changes proposed in this Pull Request:

Product brands currently maintain visibility-aware term counts through separate WC_Brands callbacks. This means callers of the shared WooCommerce recount functions update product categories and tags but can leave brand counts stale. It also makes normal stock and inventory-setting updates run a second, Brands-only recount after the shared recount.

This PR:

• includes product_brand in the deferred stock recount path;
• includes all product brands in wc_recount_all_terms();
• includes a product's brands and brand ancestors in _wc_recount_terms_by_product();
• removes WooCommerce's duplicate Brands callback registrations; and
• extends the term-function test coverage to product brands.

The existing public WC_Brands::recount_after_stock_change() and WC_Brands::recount_all_brands() methods remain unchanged for direct callers.

I found this opportunity, while I was working on #67624.

How to test the changes in this Pull Request:

1. Create a product category, a product tag, a parent product brand, and a child brand.
2. Create two products and assign both to the category, tag, and child brand:
   • Keep the first product in stock.
   • Set the second product to out of stock.
3. Enable Hide out of stock items from the catalog under WooCommerce > Settings > Products > Inventory.
4. Check the term counts under Products > Categories, Products > Tags, and Products > Brands. Confirm the category, tag, parent brand, and child brand each have a count of 1.
5. Change the in-stock product to out of stock. Confirm all four counts change to 0.
6. Change the other product to in stock. Confirm all four counts return to 1.

Milestone

• Automatically assign milestone for the next WooCommerce version

Changelog entry

A patch/fix changelog entry was created manually at plugins/woocommerce/changelog/fix-product-brand-term-recounts.

Release Communication

Select if this PR needs a generated summary for release notes:

• Feature Highlight - For user-facing features (what changed, user impact)
• Developer Advisory - For developer-facing changes (what changed, how to detect, actions needed)

Use of AI Tools

OpenAI Codex was used to implement the changes, extend the tests, run validation, and draft this pull request description. The contributor remains responsible for reviewing and maintaining the submitted code.