This statement on Investopedia is a classic case of the loose use of terminology leading to error. By “demand” economists mean the entire demand schedule or curve. By “quantity demanded” economists mean the amount bought at each price in the demand schedule or along the demand curve. And similarly for “supply” and “quantity supplied.” When a supply curve shifts to the right or left, it has no impact on the demand curve (as you point out.) But the larger (smaller) supply does push the market-clearing price down (up) as the supply curve slides down (up) the given demand curve and price does affect the quantity demanded.
The correct statement would be: “A more of good is available, the increase supply pushes the market-clearing price down which increases the quantity demanded of the good.”
An even better statement would be: If sellers want to make more of a good available to buyers, they must offer the good at lower prices to give incentive to buyers to purchase more of the good. The market clears at a lower price and larger quantity demanded.