An empty project that plays a sound effect when the space bar is pressed was used to test this. The sound effect is not played in a DirectX project on my computer, which is running Windows 10. In a Desktop GL project, the sound does play. I also tested this with FNA using XNBs built with Monogame and the SoundEffects work there, too.
Of note, however, is that Song does work with DirectX. There are a number of similar topics that have been posted about this before, but only the last topic I linked to has a solution, and unfortunately that solution (downloading a previous DirectX runtime) did not solve the problem for me. Any ideas what might be going wrong?
EDIT: Turns out downloading the latest DirectX runtime did solve the problem, but only when I used this link and not the one I found through that last topic I linked to.