If this is like every other Canon camera, Av exposes for ambient, and uses the Flash for fill. P assumes the foreground is the subject, so it exposes for that.

For your Av photo, the camera found the subject very dark, so pushed to get as much light as possible, However, the fill flash was close to the subject, so it is over exposed. You can see that the camera limited the shutter speed to 1/60 (to reduce blur from handholding) and just upped the ISO and maxed the aperture. It was dark where you were shooting, so it did its best.

P optimizes for balance: it won't let the shutter speed go below 1/60 for handholding,and it will assume you mean to expose the foreground. Usually this results in the background being very dark, often black. In your case the background is dark, but the background is close enough to be exposed a bit by the flash, so it looks better. If the background were a bit farther away, it would disappear into the black.

If possible, you can use Flash Exposure compensation in Av mode, reducing the power.

If you have Manual mode, that would be even better, as you can set your aperture, and ISO, and simply optimize yourself through trial and error (that's how flash photography works!)