Store Pages are setup as a custom page type in the WordPress engine. It is up to the theme to manage custom page/post types correctly.
Since ALL content types, pages or posts, are stored in the same place in the WordPress database it is easy for themes and plugins to confuse them if they do not query the extended data about the object.
What element types show up on the “blog list” or searches can be manipulated by the theme or plugins. I had to play with a myriad of settings to get forum posts and products to show up in the search form but NOT in my blog list. The way my newest WooCommerce theme works I even had to create a special blog category for all items (posts, pages, products) I wanted to appear in my blog list as it is setup with a “implicit inclusion” versus “implicit exclusion” rule for the blog list.
Your theme may have similar options.