If you're looking for a formalized system designed to help with some of this, take a look at TRIZ[1][2]. I'll just steal one note from the "What Is TRIZ" article - "Somebody someplace has already solved this problem (or one very similar to it.) Creativity is now finding that solution and adapting it to this particular problem."
A big part of the basic tooling for TRIZ is the results of people going through a huge mass of patents looking for patterns of problem categories and how they were solved.
[1] https://en.wikipedia.org/wiki/TRIZ [2] https://triz-journal.com/triz-what-is-triz/