You are missing the point. As is almost everyone else who says this stuff.
Most of us get paid to write software other people have requested in order to solve their problems. Every problem software solves can be solved by a sea of pencil pushers or factory line workers or human calculators or office clerks with filing cabinets or telephone switchboard operators or typists. The world used to run that way.
It no longer does because it is extremely cheap to program a computer to do repetitive actions. Compared to previous real-estate and labor-pool costs, paying even a thousand programmers to automate work done by people is incredibly inexpensive.
The problem is already solved. Your job is to translate the solution into a well-specified, easy to manipulate series of steps for a computer to execute that can be operated in production as cheaply as possible. You are literally the last step in the race to the bottom. You are literally payed to solve the problems of translating flexible human activities into code. That's the problem you are solving.
If someone asks you to program something that they don't already know how to do, then you are solving three problems - what to do, how to do it, and whether or not it is cheaper to do in software, which it ALMOST ALWAYS IS. You should be being paid three salaries - one as a business executive, one as a business analyst, and one as a software engineer.
The people pushing you to "solve problems, not code," are people pushing you to do more work in one job role to keep them from paying three people for those jobs. As a software engineer, you should be able to assume by the time something hits your task queue that others have decided that it will be cheaper to use software to solve the problem, they were competent in that assessment, and you can start executing.
As a consultant, I frequently take on all those roles for a client. But they pay me as a consultant to do those three roles. Remember that as an employee, in an extremely in-demand field, with specialized expertise compared to the rest of the work pool, you are a sole proprietorship trading time for resources. If that trade is lopsided, you need to push back and negotiate higher pay and a promotion. Don't give away work responsibilities for free because of culture hero points.