AJAX form post returns 0

I am working on a simple plugin that shows an HTML form where the user can input a keyword which is used to query an external API. I currently have the form and the related jQuery set up, but when passed to the plugin’s PHP file, I get a response of simply 0. At this point I’m only just trying to get any response but 0 (see the echo "Whyyyy" part). I’ve been scouring the internet and feel like I have tried everything that’s been suggested, leading me to think I’m making a mistake somewhere.

How do I add custom HTML to the content of an archive page’s posts?

I have a plugin with a custom post type for courses. I want to customize the content inside of the archive page’s posts and style it. I realize that the archive page is using the_content() to retrieve the posts’ content, and I’m able to use the corresponding filter to customize it; however, it’s stripping the HTML and not allowing me to style it. How do I get past this?