It sounds like you may be running into duplicate slugs. In a basic install I tried to create a Page with the URL example.com/category/ and that worked fine. My permalinks are set to example.com/category/categoryname/ for each individual category, and example.com/year/post-name/ for individual posts.
You could either try changing your permalinks and removing /category/ from them if it is there, or try combing through your database to figure out where you have a category slug. If you have uploaded a media file (jpg, etc.) that can take up a slug, as can all other post types like Post, Page, or custom post types. If WP already has one item with the slug category that is why it isn’t allowing you to create any other item (of any kind) with the same slug. It wouldn’t know which one to use.
You can always try visiting example.com/category/ to figure out whether there really is something at that URL. If not, I would try changing permalinks to see whether that resolves the issue.
Once you get that sorted, you’ll want to create a Page Template – archive-category.php is used to display individual Categories. You can either make a file called page-category.php and it will automatically apply to your Page with slug “category,” or you can make a file called tpl-category-listing.php then apply it in the editor.