You have made a few assumptions here. For starters, higher bullet velocity doesn't necessarily mean increased recoil. If the bullet WEIGHT has been reduced, the velocity can be higher with no increase in recoil. Of course pressure goes up if you just increase the amount of powder in the cartridge (or use a faster burning powder). However, 1500 m/s is VERY FAST for a bullet. For example, a good match bullet for the .50 BMG, the Hornady A-max, has a muzzle velocity of 2820 fps with a 750 grain bullet for 13K foot/pounds of energy. By comparison, your 1500 m/s (4900 f/s) bullet, if it were also 750 grains, would be a whopping 40 THOUSAND foot/pounds of energy, so THREE times the energy! Even reducing the bullet down to a svelte 450 grains would still be 24,000 foot/pounds, almost twice the energy.
Some of the fastest wildcat rounds are in the 4500 f/s range but these are usually very light bullets in a much smaller caliber. For the .50 BMG those velocities are more likely in a sabot round which would also be very light, as trying to push a heavy bullet that fast would require some very high pressures and a very tough bullet. But we can just handwave the mechanics of the gun. Since this is power armor there is probably some sort of gun stabilization system as well.
Bullet drag (which affects air resistance) is usually a function of the bullet profile, while bullet stability in flight is also affected by bullet spin and weight. In general, heavier bullets maintain their velocity better and are more accurate at longer ranges as they are less likely to deflect due to wind but clever bullet shape can offset this quite a bit.
For your scenario it would be VERY difficult for any human to make these shots without computer targeting. Various altitudes mean different air density, the higher the altitude, the lower the air density, the less drag on the bullet. Firing up or down is a tricky calculation. To have both the shooter and the target in motion is also extremely challenging. There are "smart scopes" that can sample atmospheric data (wind speed, air density, temperature) and incorporate a laser rangefinder in order to adjust the point of aim to increase the chance of a hit. But even then, firing single shots of non-guided projectiles will be of little use if the target is moving in an unpredictable way. There is a reason why almost all air defense systems use a high rate of fire to saturate the area, altitude timed exploding rounds (flak), or guided missiles.
The .50 BMG maximum engagement range for a precision shot is around 3100 meters. That is an EXTREME range for hitting a person (and is long range even hitting a plane or vehicle). So some of your engagement ranges are very optimistic. Firing from a high position all the way to the ground is also difficult. The bullet still has to travel 24,000 feet through air (assuming you are shooting straight down, not at an angle), so while it is getting assisted by gravity it eventually drops to terminal velocity, begins to tumble, and accuracy suffers. The extreme velocity of your gun would mitigate a lot of this, assuming it had a damned good bullet to take advantage of all that speed, but it is still very difficult to make precision shots 3 miles out.
What your armored flying snipers probably want is something like the Barrett 25mm XM109 anti-materiel rifle, shooting mini grenades. It is similar to the XM25 concept they wanted to field for the US Army. Fire the grenade and it is timed to explode at a specific range. You need a certain caliber in order to have an effective grenade, currently that is a minimum of 25mm or so, twice the diameter of the .50. Obviously if you had magic or advanced tech you could make the grenade smaller and fit it into the .50 round. The advantage of grenades over conventional bullets is that you don't have to hit, just get close. This is much more effective for the speeds and ranges you are looking for. Of course if the target is armored then an exploding round may not penetrate and you are back to needing a direct hit, but you don't elaborate. But the 25mm rounds could have a contact detonation option and would still be a better long range option since larger, heavier bullets tend to be more accurate at extreme range (assuming you fire it fast enough).