The camera did nothing wrong. In #1 it took a look at the entire scene, and according to it's factory programmed settings that allow for overexposure of up to 10% (or 15% or whatever) of the scene it set the camera accordingly. From the camera's point of view it did nothing wrong.

However, it doesn't know that the scene had a contrast range that was beyond it's capability, and that the sunlight falling on the bird's plumage should have received priority on exposure so that these areas would not be recorded as white without any detail - aka "blown out."

The proper exposure would have prioritized the plumage, allowed the rest of the image to be darker, and you would use your (or someone else's) post processing skills to bring the level of the darker areas up in brightness to provide an all-around well-balanced image.

There are several ways to achieve a proper capture, but some settings probably can't be improved upon much. I see that you are using a Niikon P900, which means that you are limited to shooting jpeg only. Had you purchased a camera with raw file capture capability, you might have a few more options in post processing with the enhanced ability to recover shadow and highlight information, as well as having slightly better dynamic range and more fine detail.

For this image, I might suggest a lower ISO, keeping the aperture and exposure at 5.6 and 1/400 respectively - possibly 200.

Which brings me to image 2. where the camera did exactly that, it lessened the camera sensitivity AND chose a shorter exposure, and as you can see, the overall image is better. The shadow levels can be raised and the highlights toned down a bit. There are still some highlights that cannot be recovered, on the bird's wing and the top of the head. But this is a difficult shot even with mega-expensive cameras and lenses and shooting 14 bit raw files.

The last image is fine - nothing is over or under exposed, but could still benefit from a little post processing. to improve contrast and crop the image to show the bird more prominently.

I did a quick 3 minute processing on the second image just to see how much detail was capture and to look a little more closely at the camera's capabilities. Pretty decent from what I have see so far.

What I would do differently in the future would be to evaluate the scene for things like overly bright highlights, take a test shot and use the camera's overexposure indicator (seen as blinking highlights in the preview), and use a little exposure compensation to darken the image (in this case, - 1 1/3) which if applied to the first image would give you the same exposure as the camera used to record the second image.

I've copied your camera data below. What mode do you shoot in? For very white subjects against dark backgrounds, you'll want to compensate for your camera trying to even out the exposure.

Check your camera for the "exposure compensation" feature. Try setting to minus 2/3 or minus 1 for a scene such as this.

Also, 1/125 sec shutter speed is too slow if the birds moved.

You have a bridge camera. My Canon SX50 has a burst mode that shoots with highest possible shutter speed for the conditions, while also being able to use exposure compensation. That's what I use for my eagle shots.