MacBook Air doesn’t work with eGPUs.
No, not really.
If you have an Intel MacBook Air with Thunderbolt 3, you can technically connect an external GPU enclosure, but Apple dropped official eGPU support starting with macOS Big Sur. You might get it working with hacky workarounds, but it’s not plug-and-play, and the performance gain is mediocre anyway because the Air’s weak CPU and single Thunderbolt bus bottleneck the whole thing.
If you have an M1 or M2 MacBook Air (Apple Silicon), forget it. No eGPU support at all. Apple never enabled it, and they likely never will. The integrated GPU on those chips is actually plenty fast for the Air’s use case—web browsing, light editing, office work. If you need enough graphics power to justify an eGPU, you bought the wrong laptop.
Short answer: save your money and either get a MacBook Pro or build a desktop.