I had some issues with crashes and I clicked the uninstall button and it didn't uninstall for some days as it gave some error message (I cannot remember it now) and I kept on playing and then one day it uninstalled itself. The problem is that it seems to have taken all the saves files with it! The even odder things is that the cloud saves was previously full (200 mb) but that ALSO seems to have been emptied with no clear way to recuperate it.

I was somewhat optimistic when I found this "Cloud Sync Backup saves" but no, empty.
D:\Program Files (x86)\GOG Galaxy\Games\Fallout 4 GOTY\!Downloads\!Cloud Sync Backup\saves

I have enjoyed this game so much and I have so many hours of play with my cities etc. I would be so grateful for any help.
I also checked my recycle bin but unfortunately, it does not appear to be there.

I contacted the support right away but unfortunately, zero answer.

I have the same issue right now. Did you ever find a solution?

ofcits empty. You did install Galaxy and Fallout 4 to Program Files. Reinstall evrything ENTIELY outside of System logic disc. And no to root of other discs. Use stickly this pth x/Downloads
x/Games/GOG-Galaxy/ (or Steam)
x/Games/Game-name-234/
evrything gaming related or any downloads.

For now check VirtualStore locations (there is few in Registry and folders, you obviously need folder - look to Users directory, dont forget to enable showing all folders and files).

You also can go to web version of cloud storage. GOG didnt make such option in Galaxy yet and hide it in broweser version, link hinted somewere on Support FAQ section.

Here it is
http://www.gog.com/account/cloud-saves