Truth to be told, learning Category Theory will make you a better software engineer in the same sense and to the same degree as learning Quantum Field Theory would make one a better electical engineer. It might get you more excited about your profession, but at the practical level it will be more of a distraction than an aid.
YMMV massively depending on what exactly you're working in.
I've found when I'm writing libraries that will be leveraged by other programmers, especially in a modern/high level language, insights I've derived from my understanding of category theory have been incredibly valuable.
If you're working very close to the metal (eg, embedded), very close to non-technical users (UI stuff, edge layer business logic), or in less featureful languages, then you'll get much less value.
