Where do I find loot tables in Minecraft?

The wiki documents a little bit of this on the "client.jar" page (archive) in a folded section called "File hierarchy".

The file you're looking for is .minecraft/versions/<version>/<version>.jar, that's an executable archive. When unpacked, you have a data folder that contains the Vanilla data pack. The file you're looking for is data/minecraft/loot_tables/gameplay/fishing.json or any of the ones in the fishing folder there.

And no, there seems to be no way to append to loot tables, only tags allow that (and models in resource pack have a similar concept).