I've had a back and forth relationship with the idea of design as problem solving. When I first got introduced to design in engineering school, the problem solving framing of design was what made the practice feel so approachable to me coming from an engineering mindset. Since then, I've found more comfort in design's role in asking questions rather than having answers. But my observation of professional design practice is that designers are often doing more of the "solving problems" than "asking questions."
On a Scratching the Surface episode recently, Adrian Lahoud said something that is helping me navigate that contradiction.
We think that problems are just out there, and as practicing architects we take them onboard as readymade, but the way they come to us are always structured by certain kinds of historical or political forces
Adrian Lahoud
The problem solving is dependent on the way you frame the problem, or what questions you are asking. In most professional design contexts, someone else controls the problem framing, and you as the designer are forced to solve the problem from within that box. A more complete design practice, though, is a back and forth between asking questions and solving problems. Having the freedom to choose return to the foundational questions while you are trying to solve the problem will always be more interesting to me.