My question is, if the base game is complete and free, but the expansion is in development, how should I present the game?
Depends what you want to do. Itch has no easy and ready to use dlc mechanic.
If you have a free game and make a paid expansion, then, just like that. But that is two different projects.
You can combine it on the same project if you use a individually priced file for the expansion or if you give the free base game with the demo mechanism and the expanded game as the paid version.
But what you say later does not sound like an expansion, but like an update that happens to have new content. And it depends if you want to give the "expansion" to people that already supported the free game.