As a postdoc, should I spend time learning new subjects or focus on applying what I know?
While "learning new subjects" vs "focus on applying what I know" may sound like a dichotomy at first it really need not to be one: Try to apply the things you know to new problems and learn what you need to learn to do this successfully.

Put differently: Learn new things more focused on the problems you are facing. It is really rare that you encounter a problem that you can solve by just applying what you know. In most cases, the actual problem at hand has some new structure that can be exploited in some way and this usually forces you to read up something new.

On the other hand, it can not hurt if you learn some things that are not totally related to your current research just to broaden you expertise. I do this when I got stuck on my problems and, coincidentally, it happens frequently that I stumble upon just the right thing to help me with my current problem.