Adding a discrete GPU to a 13' macbook air

No.

Apple doesn't support adding a third-party GPU to any Apple Silicon Mac – even to a desktop Mac Pro minitower that has PCIe slots.

Apple Silicon chips are designed in such a way that high-end chips (e.g., Max chips) provide very high bandwidth between memory and on-board GPU cores – the sort of bandwidth you might normally find only on discrete GPUs in the Intel world. But part of the Apple Silicon design is for all computing engines (CPU cores, GPU cores, Neural Engine cores, etc.) to share access to all of RAM. This offers opportunities to optimize away buffer copying – but assuming that Apple has taken advantage of these opportunities, it also works against being able to add eGPUs.

Apple does not support that: Use an external graphics processor with your Mac - Apple Support