Looks like you're off to a good start.
The biggest thing that jumps out is the slow shutter speed in that first flight shot and resulting motion blur. Unless we're going for a blurred background, panning shot it's more typical to shoot a large flying bird at shutter speeds like 1/2500" or faster and faster yet for small erratic birds that fill much of the frame. Yup, that means substantially higher ISO in most lighting situations but modern cameras including your Canon R6 mII can easily handle much higher ISO. You made it work better in the second flight shot, perhaps with better panning technique but at least when getting accustomed to bird in flight shots a faster shutter speed at the expense of higher ISO can yield more keepers.
The light in the first shot isn't ideal with the shadow cast right across your subject's face. Shooting subjects like that, especially with things like reeds, twigs, leaves that can cast shadows is best done in diffused light either near the edges of day or often on days with clouds softening the light.
Capturing white birds against neutral or dark backgrounds can also be a challenge in terms of avoiding blown out highlights. Hard to say if you could recover more detail in post (sometimes a bit of work with the Highlight recovery slider goes a long way) but managing your exposure to protect highlights can be important when shooting birds with bright feathers especially if they're against dark backgrounds or shot in bright midday lighting. This might mean some negative exposure compensation if shooting in an automated exposure mode (including Manual with Auto ISO) or it might mean pre-metering the scene and shooting full manual with fixed ISO which is a very good solution when the light is steady but the backgrounds change a lot like a bird flying past open sky and then in front of dark forest backgrounds.
Some positive notes include pretty good framing of a flying bird which isn't easy at the start when shooting with 500mm of lens and capturing images while the bird is flying towards or parallel to you instead of shots of bird tail feathers which are common especially when folks are just starting out with flying birds. It can be challenging with flying birds but in the first image I might have tried to place the main subject a bit off center, perhaps through a compositional crop in post and in the flight shots it's great when you can give the flying bird a bit more room to move in the direction it's flying. IOW, flying more into the frame than out of the frame but realistically the framing is pretty decent on these flight shots.
Also nice job capturing flight shots with great wing positions and against nice backgrounds which isn't always easy.
