You should be able to add Steam keys to the download page of the game and they will be distributed automatically. That would be the best solution since it wouldn't give any extra work to you (manually distributing Steam keys can be a nightmare). I recommend that you filter it so the keys are only given to the owners of the game who paid for it (not claimed it on a free sale like the one you're doing now).

Several developers are already using that system on Itch.io so it shouldn't be very difficult. I can point you to several examples if needed. Also, feel free to ask anything else if you think I can help you but there's already a lot of information given by the Itch.io platform here: https://itch.io/docs/creators/download-keys#external-keys-steam-etc

Thanks again for doing the sale, for creating the game  and for your kind reply!

You should be able to grab one now. Let me know if you have any trouble!