How do I hook the stock status message to the product page?
System Messages are printed to the page via a block (Block: Messages, Category: System).

If the messages block isn't aren't appearing on a particular page:

Check to make sure the block is added to a region in the active theme for the page in question.
Check to make sure any visibility settings for the block are configured correctly for the target audience
Make sure that your theme actually renders the region that you added the block to.

If you're still not seeing the messages block:

Create a static custom block (something that should always appear) and place it in the region.
Test with the block added to a region you know is rendering, i.e. the main content region.
Inspect the source html of the page to make sure the html is actually missing and isn't just being hidden by css.
Enable twig_debug and verify that the page is built with the templates you think it is. Check each template (Page, Region, Block, potentially others, but it would likely be one of these that's the issue) and make sure the template is properly rendering what it needs to.