I haven't shot one but the Gamo Swarm Fusion airgun is intriguing with the new gas piston tech. Their speed claims are made using their own brand's platinum pellets. The .177 pellet is only 4.7 grains and the 22 is 9.7 grains. Both of those pellets are light for caliber and produce around 16-17 FPE. Field & Stream has an article where they tested the .22 caliber Swarm Fusion with impressive results. With the .22 caliber version they averaged 890-910 FPS with lead pellets in the 15-17 grain range for around 30 FPE which is impressive for a break barrel airgun. The heavier lead pellets were also more accurate. If it were me, I'd get one in .22 as it will shoot subsonic (below the speed of sound), make less noise and have more power. You would also have a solid pest rifle capable of more than just birds if needed.
MPBR is a concept that doesn't work as well for airguns due to their often curved trajectory. Most airgunners compensate with a scope or using different aiming point (Kentucky windage) since their targets are so small. Now if you're looking for max range to use an airgun, it depends on the caliber and airgun. With that Swarm Fusion, 50 yards on birds would be a reasonable limit. If you're using it on larger pests, you would obviously reduce the range and maybe have to consider a headshot.
https://www.fieldandstream.com/outdo...fusion-review/