Hello, I recently purchased KSP on a sale, and I've been playing for the last few days. I decided to get the two DLCs that were released (Breaking Ground and Making History), but after purchasing, I haven't been able to figure out how to add them to the base game. When I go to the GOG Galaxy app and click "configure-dlc", it doesn't show anything. I know the order went through, because my order history shows it. Do I need to uninstall and reinstall the base game or something? Thanks.

Nah. Just use the offline installers.

I would expect DLC to be treated as patches, and unless you changed the default settings to apply
automatically in the background.

Did you check the "Extras" button in Galaxy? The offline installers are listed there ( including DLC ).
Is there a way to check in game?
Did you try relogging (into Galaxy)?
Did you check your web login?