I cloned the repository and did ./gradlew build. Which folder is the actual API in? Would it be this: fabric-api-0.32.9+local-1.17.jar ?

yes, but why are you building from source?

I have a script that builds all the mods I use on my server.
Obviously, I need the Fabric API as well.

It is just the easiest way to update everything.

Ah ok. then yeah, the file is in build/libs

Thank you!