At the bottom of the Settings >> Media page(/wp-admin/options-media.php) you can choose to start organizing uploads by date or not. Not having the date folders for uploaded files makes it much easier to move media libraries to new sites like you’re doing. That previous dev set you up good.
If you tried to upload all the images via the media library so they could be managed there, they would all be stored in a different date folder than the old blog posts are linking too, so even though they are managed in the media library, all the old blog posts would have broken images.
If you turn off that setting for date uploads, then you could bulk upload all the images using the media library, and the images will be managed in the media library, and the blog post images should still hook up properly if they have urls like yourdomain.com/wp-content/uploads/some-beautiful-image.png.