Best way to add sound to a project using a by8301-16p?

Forget about your servo and LEDs and sketch for now. You need to start by just getting the sound module by itself working, then once it's working perfectly by itself you can integrate it into your project.

So disconnect everything except for the sound module from your Uno and then try the "super_simple" example the library came with. Make sure to set up some sound files with the filenames the sketch is expecting.

That sketch is only for use with Arduino boards that have a second hardware serial port. The Uno only has one serial port. For the Uno, you would need to use the library's "SoftwareSerialExample" example, but that also requires you to modify the library source code.

My recommendation is that you focus on one library at a time. So start with trying to get the first library working by itself. If you never have success with that one, then you can switch to trying to get the second library working, again starting with the most simple example and the sound module alone, only switching to integration with your servo and LEDs sketch and circuit once the simple sketch is working perfectly.