WordPress blog posts template bug [closed]

You’re not supposed to see the template dropdown when editing the Posts page, because changing the template with the dropdown wouldn’t do anything.

The template for the Posts page is determined by the Template Hierarchy. When you make a page the Posts page it’s no longer a Page in terms of templates. It will use home.php template if it exists, or index.php if it doesn’t.

If you want the user of your theme to be able to select different templates for the Posts page, you would need to implement that yourself in a custom meta box or the Customiser.