Does anyone know if playing games on Steam and GoG Galaxy uses bandwidth?

Depends on the game, I guess, though that's probably more a game issue than a Steam/GoG one. The biggest menace is when they arbitrarily decide to do gigantic updates: not so bad now that I'm unmetered (albeit on a 14 Mbit length of wet string) but when I was on a metered plan it got pretty close more than once.

Multiplayer will use some bandwidth. For single player games there should be minimal bandwidth used for achievements, etc, but the main usage (other than game updates) would be if cloud saves are enabled.
By default Steam will download game updates in the background while you are playing, but there is a setting in the options to disable that.

For the Divinity games, you can exit out of Steam/Galaxy and start the games directly from the respective executable. The passive client functions shouldn't use a significant amount of bandwidth, though.

Thanks; I do have cloud saves activated. I just noticed that for the last three weeks or so, when my generator has been down so unable to game, that my usage has been cut in half. I'm allowed 10Gb per month before being throttled. I'll deactivate cloud saves and see if that helps. Really, what does having GoG galaxy do for me, anyway? I'm not interested in (is it) exploits so I may as well play the Divinity games without using it. I do have auto updates inactivated - I'm not sure about Divinity games but, for some, a new download causes severe issues. I do the updates between games.

Galaxy supports multiplayer lobbies, chat, achievements, game updates and rolling back to previous versions. Galaxy updates are a day or two faster than patches, since developers can upload directly, but that doesn't matter if you are waiting anyway to get feedback on updates, and if you are keeping the patches you can effectively roll back by uninstalling the game and re-installing (or reverting to a backup of the game folder made before updating).

The next version of Galaxy supports managing games on different platforms, and they are planning cross platform chat and some other features.