I recently installed Pharaoh New Era, and resumed playing GOG games after a hiatus. Today I am getting a message that my cloud storage is full; I have 400 MB allowed but the message says I'm using 3 533+ MB.I have only two 300kb save files in P:NE at the moment. How can this be happening?

I played P:NE successfully for several hours yesterday, with up to about a dozen save files at the max. I have a lot of GOG games installed, so I wonder if maybe there are more files in other cloud-saved games that suddenly started syncing when they hadn't previously? I knew the old Pharaoh/Cleopatra had cloud save so I deleted most of those, but I *think* the 3 533 number didn't change. Do I need to go through every GOG game to delete unused save files?

The error message is probably global, not game-specific.
Cloud storage could be filled up with data from a game that you uninstalled. If you can't find an installed game with a large save collection, try opening a support ticket. There's no way to manually manage your cloud saves (other than downloading a backup copy for each game).
If you've played lengthy, complex RPGs that can take hundreds of hours to complete, those can have large save files. I've also heard someone say in some cases, the entire game data folder gets synced, including things like screenshots.

Honestly, ask yourself if you really need cloud saves. If you don't play on multiple devices, I'd say no. You can disable cloud saves under cogwheel - Settings - Game Features.