The “Unclustered files” you see is not a folder on your hard disk and Picard won’t create it. That is just how Picard organizes the files in its user interface: On the left you get files you loaded into Picard that have not yet been matched to a release n MusicBrainz. Those are by default in the “Unclustered files” category. You can use the “Cluster” button to organize the files by album.
To get the files to the right you have to match them to a MusicBrainz release, either by using the Lookup, Scan actions or manually via searching. The recommended workflow is to first cluster the files, the try “Lookup” and use “Scan” for the difficult cases. For details please see the following documentation:
Of course you can also keep the files on the left pane and manually edit the tags, but Picard’s main purpose is to update the tags using data from MusicBrainz.
Whether Picard creates folders and how files and folders are named is controlled by the settings in Options > File naming. If you don’t want to change your folder hierarchy and file names, disable both “Move files when saving” and “Rename files when saving”. Make sure to enable Options > Tags > Write tags to files if you want the tags to be updated.