ATT = .ai Adobe Illustrator Files
The Logo (all versions) and Media Kits are Illustrator files.
For the logo, you can export any artboard in a variety of file types depending on your needs.
You will need to have a licensed copy of Adobe Illustrator to view and edit, which is expensive. However, you can also download Inkscape which is free and open source to view and edit.
wix media files
You also have all the website versions of your logo in your Wix Media Files. Those images can also be downloaded.
Simply select an image and click the 3 dots and select download. Most of the website logos are transparent PNGs.