The only difference I’ve noted is that the recent project saved with the extension .scrivx while previously everything had .scriv extension.
If you’re looking at Scrivener’s storage folder in Files.app, then that makes sense. If you have a bare “.scrivx” file in there it explains why the iOS version cannot do anything with it. That’s not a project, it’s just one file that describes the binder. Sounds like not enough got dragged between folders, on the PC side. You would want to copy the whole project folder, just like you did with the other projects.
Is there an option to use something other than Dropbox?
Yes, the user manual has a number of methods described, in §14.2.3, Managing Projects Directly. The method that I often use myself is most fully describe in this thread.
When I’m not using that, I am using iFuse, which lets you attach the device to your computer directly like a disk (no jailbreaking necessary). With that I can load projects straight off of the device with the desktop version, rather than copying things around, but that’s also very easy to do as well given the nature of how it works. I don’t know if that tool specifically is available for Windows (I use it with Linux), but it wouldn’t surprise me if there was something similar, if not.