Firaxis Games has announced a new Civilization VI update that allows cross-platform cloud saves between steam and Nintendo Switch.
You will have to create and link your 2K account to the game to enable this feature.
The update for both Steam and Switch versions has added a new menu option called "Multiplatform Cloud". When saving a single player game from Steam, for example, you will be able to save to "Multiplatform Cloud" and resume playing your game on the Switch.
Cross-platform saving is only available for the base game at the moment (PC players will have to disable the expansions to get the cloud save feature to work) and will not work with any of the expansions.
The PC version you will need to use is 18.104.22.1684 or newer, and the Nintendo Switch version you will have to use is 1.0.3 or newer.