Hello, I noticed that your contest is still open after 5 days. I bookmarked it since I was, at the time, busy with another job, but currently, I am available. Here I send you my proposal since you have still not closed the project.
How important is security in your app? I imagine that you don't need special authentication or encryption since you need this to be over WiFi, but still.
I have already built a similar app, remote control, java desktop app that implements a socket server, and a client that is on a mobile phone. For your app, of course, it is the opposite of that, the Android app hosts a server. The desktop app can have a JavaFX GUI or simply be commanded from the terminal, depending on what you prefer.
Overall I believe that it can be fully built about 7 days from scratch.
I wish you all the best and a nice weekend, hope to talk soon. Br