Ridiculous take home tests are probably the number one reason I decline to continue interview processes. If you think that building a client, an API, wiring it up to some other third party API, then deploying is a reasonable scope for an unpaid interview challenge then you are very bad at scoping software projects and the most important thing I can do for you is tell you as much.
I told one start up if I built what they asked for in the interview, I would pursue funding from their investors and launch it as a competitor- it was that similar to what their actual app did.
I did one where I went through a few rounds of interviews, technical and otherwise. In talking with the developers, they mentioned that they were trying to integrate a certain client side framework into their backend frameworks build process, without success. Get to the final stages, and the director of engineering asks me to work on this take home project to, you guessed in, integrate the js framework into the build process of the backend framework.
I sent them a strongly worded rejection email. It was a realreal eye opening experience.