When does separating digital and analog ground make sense, is it essential, and when is it not? Should I separate the grounds in this project?
There are different views on the problem. Holy wars were fought on the issue.
It's somewhat right and somewhat wrong. It is right to keep the return paths separated but how do you handle the transition points, i.e. ADCs DACs and mixed signal component in general?
The current view for complex boards is to keep one single ground plane (or ground mesh) and partition geographically the board in analog/digital/power/RF section to keep in check the return currents.
That said, your circuit doesn't seem to need a very performant ground system so it doesn't really matter. Just be sure to pick a point where join the two ground networks (that's essential, there must be a DC path between the grounds)