Photos won't import photos - says "Unsupported file type"

I'm unable to import some photos into Photos.

I've got some photos a friend sent me; I think they were extracted from a ZIP file or something like that, with Unarchiver (they've just been sitting in a folder for a while). All the files have suffix JPG, but Finder calls them "TextEdit.app Document". I try to import them into Photos, and I get "Cannot Import Item / The item cannot be added to your Photo library because it may be an unrecognizable file format or the file may not contain valid data." And below that, it lists the file name, and says "Unsupported file type." In Finder they look like totally normal pictures.

If I Get Info, I'm able to change the file to "Open with Preview.app" (or Photos). If I do that, yes, I can open them with Preview (and they look like normal pictures) although MacOS first gives me a warning that it "may be an app". If I open in Preview, the picture looks fine, but I can't save it - it says I don't have permission (even though I do).

After I've changed the file to Open with Preview (or with Photos), I still can't import them into Photos, and get the same warning.

So ... they're weird files, and I want to add them to Photos, and I can't. Help?