3dscapture.com

Looking to buy an original DS capture card! Anyone selling? Need for GBA streaming.

This might be a cheaper option for you if you’re looking for GBA streaming only. I have one of these and they work great.

https://www.epilogue.co/product/gb-operator

That product seems to just be a cartridge dumper with a nice interface, it's still using emulation to play the games. A DS flashcart can also dump games and saves from the GBA slot of a DS or DS Lite, and the newer unbranded ones are around $10.

There's a few other options for high-fidelity GBA capture, but you'll need a capture card for them:

A modded GameCube with the Game Boy Player using GBI instead of the Game Boy Player disc, with digital AV-out into a GCVideo hardware solution to cleanly convert to HDMI.

A GBA Consolizer, currently available through GameTechUS and, recently, from Gamebox Systems as well. The latter doesn't seem to have room for the GameCube link cable, since the other ports are placed too close to its link port.

If you're just looking for GBA streaming, these might be nicer, as they provide easy external controller support and link port functionality.