Appreciate the PR! Would you mind dumping and sharing output before/after of a site with WooCommerce menu items?

Thanks, sure. Here's the output on /shop/ — wc_get_page_id('shop') returns 10.
Before (without wp_nav_menu_objects filter)

{
  "active": false,
  "activeAncestor": false,
  "activeParent": false,
  "classes": false,
  "dbId": 53,
  "label": "Shop",
  "object": "page",
  "objectId": "10",
  "url": "https://johanneshof-reinisch.test/shop/",
  "children": []
}

After (with wp_nav_menu_objects filter applied)

{
  "active": true,
  "activeAncestor": false,
  "activeParent": false,
  "classes": false,
  "dbId": 53,
  "label": "Shop",
  "object": "page",
  "objectId": "10",
  "url": "https://johanneshof-reinisch.test/shop/",
  "children": []
}

objectId: "10" matches wc_get_page_id('shop') — WooCommerce's wc_nav_menu_item_classes() correctly sets active: true on the Shop menu item via the wp_nav_menu_objects filter. Without the filter, active stays false even on the Shop page itself, because WooCommerce renders it as a post_type_archive('product') and core's _wp_menu_item_classes_by_context() doesn't recognize the page-type menu item as current in that case.

thank you!