When using the product search widget in my PRO header, it ignores that we’re shopping in the store.
I’d like them to be able to return to the main shop easily with a breadcrumb if possible.
Since the breadcrumbs in the theme is only applicable to built-in post types of Wordpresa and theme itself, then you’ll have to create a custom code to include other linking to the breadcrumbs. Please check this as a sample
The indexes such as [0], [1], and so on represent the breadcrumb items. And you’ll have to change is_page() as condition with is_search() with post type. Example