I also have this problem. I converted a Picture Book to digital for a friend, and it had a lot of high resolution images. The document is set to prefer linked images, and the resource viewer shows the images are linked, but the document takes several seconds to save and is 1.6gb, so presumably the images are getting embedded somehow. This occurs with 1.7.270 and 1.7.283.
It looks like Affinity Publisher just embeds the full size images regardless of whether or not you choose to link, since even when I open the file without the images being in a locatable folder, they still load at full size. If you must store image previews, it might be better just to store thumbnails if the image is linked rather than embedded.
I found this relevant forum link regarding file size with Affinity Designer, so perhaps the work on this issue is yet to have been tackled, but I hope it is soon:
I also noticed that Publisher is using absolute file paths for image location, but relative paths seem like they would work much better in most cases. I guess it really depends on how the images are stored. I personally just link images that are stored in a folder in the same directory as the afpub file, so it's easy to move everything around, but I suppose some people might use images on a network drive or something, so in that case, absolute links would be better. It would be nice if users could easily change the root folder in which to look for linked images.
Aside from this and a few other bugs, Publisher has been pretty great so far. Looking forward to the final release!