Interesting definition. This applies to almost literally nothing except Jefferson’s candle and IP. Actual literal fire is considered worthless and IP is bazillions of dollars of closely guarded secrets. Public transits, seemingly unlimited water sources, or neighborhood parks all suffer from overcrowding so this diminishing availability thing is tough to meet
It is the actual definition since economist Paul Samuelson coined it in 1954.
Things like public parks and public pools would be classic examples of a "Common resource." Rival and non-excludable.
Classic examples of true public goods would be public radio broadcasting or national defense.
At some point in the past couple decades, people have come to misunderstand the term. Having heard the argument that public goods justify taxation to fund them, they come to believe that anything they like must be a public good.