There's a way to create a giveaway with gifts that are no longer available on Steam?

i believe you cant make giveaways with gifts in your steam inventory.
better gift them to friends.
and if you dont have friends, you can always add me on steam and gift them to me.(thats a joke)

I guess you can gift it to a friend or just trade it with someone else.

Create a new Support Ticket and select Add Game to List.

Did the game become free to play before getting removed by any chance? There might be a reason it's removed from the list. Checked your inventory but gifts are not visible so can't tell which games it's about.

A game like AERENA for example became free to play, but now the plug is pulled completely. And from my understanding it was a multiplayer only game so not much point in being able to give it away.