SquareSpace does not offer any way to export uploaded content directly. The only export option available is for WordPress, but this only generates a small XML file. What is the best way to download the actual image files from a gallery, other than right-clicking each image and choosing "Save as..."?
I just spent way too long figuring out how to do this, so I'm leaving this here in hopes that it will save someone else time. It's not pretty, and it involves a browser extension, but I believe this is the most efficient way. Broadly speaking, this is what the process looks like:
Repeat the following steps for each gallery:
That's it. All said and done, it's a pretty simple and straightforward process. I went through a lot of different WordPress plugins in an attempt to rehost the external links to the local wp-content folder, export the media library by post, etc. This ended up being much faster and much simpler. Hope it saves you some time.