The debug log says that the library is stored in "Amazon/.Kindle Library". I am not sure if the Amazon is in the path cloud path.
The calibre library is opened 17 times (in this log). The first one was at 2016-08-09 17:13:44.094. This was the first time the library was opened, and the metadata.db file was transferred. The metadata.db file is dated 2016-08-09T18:45:42.526Z
From then on Amazon reports the same modification time for metadata.db. Example: amazon currentRev=2016-08-09T18:45:42.526Z, lastRev=2016-08-09T18:45:42.526Z. I think we can safely say that the metadata.db file isn't being updated, which is consistent with what you saw.
I did a test using the Amazon Cloud client. It refused to modify my metadata.db file, saying that a different file was already there. I manually deleted metadata.db from the cloud then did a sync, and the file updated. That isn't a sustainable process, because (apparently) none of the files in the library will be updated. Of course, you can be sure that the cloud library is up to date if you delete it from the cloud and re-send it in its entirety. Also not a sustainable process.
There are some third-party apps that sync with amazon cloud, such as syncbackpro and goodsync (neither seems to be free). Something called "odrive" claims to sync, but it isn't obvious what it does.
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