Short Chainstays like said make the bike more maneuverable, you can steer more with your hips. Short is subjective. It depends on height. The taller you are the longer the bike, Im 5'6" so 420mm or under is short. If you're 6'+ , 435mm will feel similar.
Poppy is not enough rebound in the shock and fork, so you use them like pogo sticks.
Like you i enjoy my bikes to feel lively if this is what you mean. I also enjoy climbing so my 3 bikes have that light front wheel feeling. Playing with selection of saddle, tuning of the cockpit can change a bike quite a bit. Put on a shorter stem, a narrower bar and take a bike and make it your bike. If you focus on a single factor i am not sure you will enjoy the bike you will select. You can buy a quality bike that is 3-6 years old and if you do not enjoy it you can sell it with very litle loss. Tires, transmission etc.. are also key to feeling you are on the proper bike. Personally i also use a riser bar.