You dragged the files from Local Sites/site_folder/app/public onto your desktop and then dragged them back to the same folder? That process shouldn’t create any issue. But I see your Local Sites shows 2 sites with the same name.
I’m apparently failing to understand the situation well… But just describing: You had one site, you wanted to export the website, so you opened the site folder on Local Sites and dragged the entire folder of your website to the desktop, then dragging it back on Local Sites folder once you saw it wasn’t right.
If that’s so, it seems like Local is reading your dragged folder as a new website import.
The manual export method involves a zip file with the contents of the app/public folder and a database.sql (which is the database dump that you can make from Adminer) files inside it.
To describe Local by Flywheel “automatic” export method, you just right-click on the site’s name on the app and click “Export” and it will create a zip file with the files and database inside.
Both zips (from manual or “automatic”) can be dragged directly inside Local’s app and be imported as a New website. If you want to “override” the website, you will need to delete the old one, and import the new one (but just do it if you know you have the right export file).
This post below may help you:
Just be careful to not lose your work. If you delete your website without a proper backup of files and database, it might be really hard to recover it.
If you have any trouble or questions, just fire away, I’ll be notified 