Abstract Algebra, looked at through the lens of Programming, is kind of "the study of good library interface design", because it describes different ways things can be "composable", like composing functions `A -> B` and `B -> C`, or operators like `A A -> A`, or nestable containers `C> -> C`, with laws clearly specifying how to ensure they don't break/break expectations for users, optimizers, etc. Ways where your output is in some sense the same as your input, so you can break down problems, and don't need to use different functions for each step.
Category Theory's approach of "don't do any introspection on the elements of the set" led it to focus on some structures that turned out to be particularly common and useful (functors, natural transformations, lenses, monads, etc.). Learning these is like learning about a new interface/protocol/API you can use/implement - it lets you write less code, use out-of-the-box tools, makes your code more general, and people can know how to use it without reading as much documentation.
Focusing on these also suggests a generally useful way to approach problems/structuring your code - rather than immediately introspecting your input and picking away at it, instead think about the structual patterns of the computation, and how you could model parts of it as transformations between different data structures/instances of well-known patterns.
As a down-to-earth example, if you need to schedule a bunch of work with some dependencies, rather than diving into hacking out a while-loop with a stack, instead model it as a DAG, decide on an order to traverse it (transform to a list), and define an `execute` function (fold/reduce). This means just importing a graph library (or just programming to an interface that the graph library implements) instead of spending your day debugging. People generally associate FP with recursion, but the preferred approach is to factor out the control flow entirely; CT suggests doing that by breaking it down into transformations between data structures/representations. It's hugely powerful, though you can also imagine that someone who's never seen a DAG might now be confused why you're importing a graph library in your code for running async jobs.