I would actively seek assignment to a project! At least in the case that you want to stick around and be valued by your employer. I always am searching for more work at work whenever My current project(s) are in a lul. Employers value self motivation.

On the other hand, if none of the work available at your company interests you enough for you to want to pursue it, you probably should be looking for a new job.

Also, I limit my side projects' leakage into the work day to a few peeks into API docs or datasheets, anything more is inviting trouble.