The open source project I stumbled upon that allows you to run Android apps on PC is Waydroid....it takes a container-based approach to running a full Android system directly on Linux
I'm having a look at documentation about it and weston does indeed seem like a pretty straightforward way of having a Wayland compositor on top of X11 (or per the documentation, on top of pretty much anything) to run applications that expect such a compositor, like Waydroid.