single-{post_type}.php is not loaded despite flushing rules

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Flushing the rewrite rules – which you can do just by visiting the Settings -> Permalinks page – was a good step to take, because it’s usually the overlooked cause of these sorts of issues.

However as Milo said in the comments, in this case, it’s just that the publicly_queryable argument needs to be true if you want these posts to display on the frontend.

From the docs for register_post_type():

public
(boolean) (optional) Controls how the type is visible to authors (show_in_nav_menus, show_ui) and readers (exclude_from_search, publicly_queryable).
Default: false

publicly_queryable
(boolean) (optional) Whether queries can be performed on the front end as part of parse_request().
Default: value of public argument

As you can see – and again as Milo said – just avoiding setting publicly_queryable will make things a bit simpler for you in this case.

I would definitely recommend reading up on those docs to understand what each of the attributes do, but I realise it can be difficult to get your head around at first!

As for your second question in the comments:

Does public affect if the template is shown? And has_archive or rewrite?

  • public is a quick override to generally control all of the backend and frontend visibility of your post type in one go: unless you override it with any of the four more explicit options as seen above. For the frontend, these are publicly_queryable, as we have already addressed, and exclude_from_search. You’ve already set exclude_from_search to true, so no matter what you set for public, this post type won’t be found in searches (OR taxonomy term lists).

  • has_archive won’t affect whether your single post types can be viewed, but it will turn on and off the option to view the archive ‘loop’ of all of your posts – at http://example.com/your_rewrite_slug

  • rewrite doesn’t affect public visibility of your posts; just what the URL will be. The URL has to be something though, so if you don’t set the rewrite value, it’ll just default to your post_type name – in this case ‘producto’

Each of these are also covered in the docs, so I’ll mention again – definitely read up on it. The investment will be worth it! 🙂