If you have "Alan Wake Franchise", you can still enter the giveaways for it !

There's tons of giveaways that can I can apparently enter even though I've synced my account.

That because the franchise is only a name for the store edition, but in library it will be named 'Alan Wake' while including all the things.

Steamgifts plus. Use the filter. Works like a bomb (plus you'll never accidentally enter a Bad Rats GA...)

Same with Serious Sam and Half Life Complete Packs

Maybe we should make a list of such games, if there is not one.

It's the case with pretty much every package. The package name isn't what's reported by Steam, but the individual games in it. As with most DLC, there's no way for Steamgifts to know if you already have the entire package or not.