Custom Posts don’t use custom static page template files. Custom Posts have their own template files for custom post archive index pages and single custom post pages.
For a single custom post page, you need to create a single-{post-type}.php, which for you would be single-project.php.
Similarly, for a custom post archive index page, you need to create a archive-{post-type}.php, which for you would be archive-project.php.