When I go on the editor I see a list of placeholder blog posts from the template, but I don’t have the option to delete or add new blog posts. This also happens for regular pages, I don’t see the option to add new pages.
Click Collections, than Blog Posts, and add them there.
The view you’re looking at is a view of the pages that exist on your site, which includes collections pages. You can use it to navigate to existing things, but not to create new ones.
Under Collections, you’re working with your CMS data directly, there you can add / edit / delete.