Find games that haven't been given away before?

This system will be like the bundles list, except like you said, you need to cross-reference givenaway games. But how often? Simple logic, you could say, "After every giveaway is created.", but doing that would require you query a really big string dump and processing, and an unnecessary one.

Right now I believe the Steam API is queried at every set intervals, like every day perhaps and the game library you see when creating a giveaway is retrieved data from the local database. Which is not that much of a thing(And yes, I do not think the daily update is a COPY of Steam API query. Pretty sure it's filtered out AND processed before being inserted.). You query one string and fetch the data with that filter. Otherway around you query thousands of titles against way more than thousands of titles EVERY TIME to keep it updated. So yes, either ways this would require almost constant synchronization with Steam API, which would be waste of resources imho.

You could however do something easier, populate all the latest giveaways from the local database and put them together in a list. So you can look it up yourself if it was given away or not. That wouldn't be that much resource-tiring process.