Sometimes you can find pre-patched ROMs, but it's rare.

Patching a ROM yourself is pretty easy though. In this case, the site you linked has a patching tool built-in. Just download and select "patch" then upload the original ROM.

Is there a reason you can't just patch it yourself?

I have gigantic archives of pre-patched Roms on Internet Archive; that is Roms with the patch on it already. But I can't link it here I think. The problem is, distributing them counts as piracy, because it contains the game itself. That's why you see the patch files distributed like on Romhackplaza.org and Romhacking.net .

I want to know how to play the real thing with a gyro controller.

In mGBA You can map it to an analog input, and have gyro be an analog input with steam input. But it didn't work right on my Steam Deck.

Probably, but telling you where to find it would be illegal in many countries (depending on instance country and applicable law, hosting comments or messages containing such information could be considered copyright infringement). Patching your own legally obtained ROM is pretty easy, though.