"The quantity supplied refers to the amount of a certain good producers are willing to supply when receiving a certain price."
Leave aside the error of assuming only producers can supply anything, and notice the wording: "when receiving a certain price." That means the "producers" ARE SELLING the good at that price.
Of course there is no contradiction between the definitions. The conflict is between what you claim they say and what they actually say.but I accept it, just as I accept this definition from Harpers (same link as before):
For me there is nothing contradictory between the definition you cited and the one I just cited above. Is there a conflict there in your mind? Is there anything wrong with Harper's definition that you can see?
FWIW, a lot of definitions of supply talk about "amount available for sale," but I reject that formulation as it defines what is available for free as not being part of supply, clearly a nonsensical notion.