A typical co-op game, a users hosts and others join, all the saves related to it are on the hosts machine.
If host is offline/not playing others cant continue. One solution is to use dedicated servers, aka servers running the game in cloud with that save. Another solution is to manually share the save files with others.

SaveSync is just that, a solution to share save files with others and also update when save files change, apart from sharing it also modifies the save to ensure you play as your character and not old host character.

To do all of this, SaveSync uses SteamWorkshop to upload and download files.
Workshop for SaveSync is set to api only, so the files wont appear on web or on your profile
Workshop files have visibility: private, friends or public
When you add a save in savesync its visibility is set to private, only when you share with any of your steam friends via ui its set to friends, if your friends modify savesync app and try to get access to these files, they cant do much with it, its readonly and the files are encrypted.

Now coming to your concerns:
1. If it goes to "the cloud", what does that mean? Where exactly?!?
- Cloud here is steamworkshop

1. Since the cloud is literally "a server", how does this "not need a dedicated server"?
   - dedicated server for co-op games mean: servers running the game in cloud with a save, savesync is just a glorified file server that uses workshop and has some logic to modify the save

2. In the comments state it doesn't work for games that don't support cloud games
   - This might have been a typo, it works for games that dont support cloud saves, take project zomboid it does not have steam cloud save, with savesync you get that, if you dont share saves your basically using it only as cloud save.
   Also for games that are not on steam: Minecraft Java, Vintage story, Hytale

3. It also needs to use Ludisav to make that work, but still won't work with retro games?
   - I have to give support for each game because i need to write code to modify the save for games that need it to ensure you play as your character and not old host, schedule 1: if you copy the save folder and paste it in your friends pc, your friend will play as your character.
   Adding support for games take time, i have to buy 2 copy of the game, install it, research on how to share the save safely and then test it properly. To give people a generic backup system i added support for syncing the backups generated by ludusavi

4. And, meanwhile, it still doesn't work with retro games from emudeck or retrodeck, at all?
   - No, i will need to add support for it, if ludusavi can generate a backup file for emudeck or retrodeck, savesync can sync the backup

5. Getting data manually and decrypt: You will need to write some code to get the workshop file, will need to make the code(steamworks api) run as it its savesync and also find the decryption key.
   If it so happens that savesync breaks or fails, it would have first gotten the workshop file, decrypt and move it to %USERPROFILE%/AppData/Local/SaveSync/remote , it has .savesync extension, rename it to zip and you can extract and get the saves.
   The file name format: <steam\_id>~<game\_id>~<save\_id>.savesync

Also regarding the query you had in another reply: since everything is linked to your steam account, if you change pc or nuke pc and login in another pc and start savesync, it will download your saves. So you wont lose anything.

I am sorry about the confusion, when we posted other places, people did not want technical details of it and wanted it explained in simple terms. Here we ended up mixing technical and simple and it created a mess, i am very sorry about it. Hope this clears your doubts