On a world with a third of Earth’s surface gravity, with an atmosphere with the same pressure, makeup, and temperature as Earth’s, could pedal powered aircraft be a viable and easy method of recreational transport?
The Ole Ornithopter comes to mind :p https://www.britannica.com/technology/ornithopter
As you've specified that air pressure is the same as on Earth, achieving flight would be much easier - as any attempt at flight would achieve the same amount of lift as on Earth while only having to deal with a 3rd of the weight.
While I lack the engineering background to do the math, by looking at the behavior of squirrel suits, paragliders and model airplanes, I think you'd land up with the situation where small, very fit people would be able to maintain flight while large people wouldn't. Which would result in a very interesting dynamic where short people would have potential societal advantages as opposed to how tall people benefit in our societies.
Another aspect you'd need to decide on would be whether human's bones are as dense as they are on Earth. People in space (or the Moon or Mars, ect) actually suffer bone mass loss due to the lower gravity - which is fine so long as you don't return to a higher gravity planet again but actually makes achieving flight easier as you weigh less from the bone mass loss.
Finally I think an important halfway point needs to be mentioned here. Same air pressure and a 3rd of the gravity means a much lower terminal velocity - max fall speed. This means that falling would be much safer, potentially to the point where normal humans wouldn't risk injury by jumping off a 2 story building. In this environment, even if not everyone could achieve permanent flight by pedaling, "falling slowly" is going to be a very common means of transportation down hills, between buildings or even long distance by going up an elevator and "falling slowly" towards the next elevator.
Here on Earth, we already have seen many examples of human-powered aircraft. With a third the gravity, we would see reduced weight on the aircraft, making it easier to get off the ground than it already is. In here, it says that someone with average athletic ability could fly a particular aircraft, so it is not unreasonable that flying could be accessible to the average person. It could be like riding a bike, something you can do casually and also train for if you want to fly faster and longer. It can be imagined that piloting your own plane is like cycling.
I also think Alot has a good reply with the safety of flying such a plane. With lower terminal velocity, combined with the low speeds (I'm estimating about 30 to 60 km/h based on some of the speeds I saw), it isn't too dangerous if everyone goes about flying with proper regulations. Maybe there can be air-lanes to the tune of bike lanes, or designated areas to fly in without having to worry about air traffic regulations.