I think that the most plausible way that Category Theory is going to improve your life as an engineer is that it will sneak into the way your tools are designed.
You don't personally need to know about the Yoneda lemma to benefit from a better designed programming language whose type system was informed by algebras of types, allowing it to leverage exhaustive pattern matching.
With that said, learning about techniques used in functional programming that have their origin in category theory (maps, folds, algebraic data types, monads, monoids, etc) can allow you to think about how to solve problems (even in non-functional languages) in ways that can be more "natural" to the problem, in that the abstractions used resemble the problem description more closely. That ability to decompose difficult problems in new ways can definitely make you a better engineer.
You don't personally need to know about the Yoneda lemma to benefit from a better designed programming language whose type system was informed by algebras of types, allowing it to leverage exhaustive pattern matching.
With that said, learning about techniques used in functional programming that have their origin in category theory (maps, folds, algebraic data types, monads, monoids, etc) can allow you to think about how to solve problems (even in non-functional languages) in ways that can be more "natural" to the problem, in that the abstractions used resemble the problem description more closely. That ability to decompose difficult problems in new ways can definitely make you a better engineer.