Title. Says they are saved to the cloud. No syncing is occuring. Cannot find them anywhere. Really really really annoying.

there is no cloud save... they are stored in a local folder

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You literally have the ingame option to save to cloud and GoG supports cloud saving.

I also don't have working cloud saves, despite a supposed in-game checkbox to toggle. There are no options in Galaxy for cloud save sync, etc. I've submitted a support ticket to fix the game card.

Paradox used the steam server for their cloud saves in Rome & Stellaris so yes if you get the game on steam or you can pay for it in gog and use the key to unlock | play with the Paradox install... both have cloud saves
However
the Galaxy verson doesn't have cloud saves yet... the paradox code moves cloud saves to a folder on your local hard drive & that may or may not be something on their list of things to fix but Paradox doesn't have a large IT section and they have other things on their "to do" list so your guess is as good as mine as to when that could be

I got a reply from GOG: This game does NOT have Cloud saves. It may have saves that Paradox manages, but it doesn't use cloud saves as we're familiar with them.