Intelligently detect product search fields and restrict results in Autosuggest

[brandwaffle]

Is your enhancement related to a problem? Please describe.

Currently, WooCommerce product searches show results from the default Autosuggest query, but then a full search (hitting enter to reload the search page) does limit the results as ?post_type=product is passed into the URL and therefore handled by EP properly.
Describe the solution you'd like

Determine when we're on a product search bar when applying Autosuggest, and conditionally limit the search to the product post_type.
Designs

Describe alternatives you've considered

Additional context

This would be a permanent/plugin-wide fix for the issue resolved with custom code in #1684

[Rahmon]

A possible workaround here could be to restrict the post type to product when accessing a WooCommerce page:

add_filter(
	'ep_term_suggest_post_type',
	function( $post_types ) {
		if ( is_woocommerce() || is_cart() || is_checkout() || is_account_page() ) {
			return [ 'product' ];
		}

		return $post_types;
	}
);

[JakePT]

@brandwaffle I've updated the PR #1689 to bring it up to date with develop, and improved the handling of post type inputs in the search form.

@Rahmon I think the issue with that approach is that searches for products aren't necessarily coming only from WooCommerce pages. For example, it's common for shops to have a product search form in the header that only searches the shop, and there's no guarantee that WooCommerce pages don't also have a blog search form or similar. The approach in #1689 handles both those cases.