What is culture?
People are conscious. Occasionally. Consciousness is great for problem solving, but not for execution. We learn concepts and skills consciously, but later apply them without explicit thought.
At least while the skill works. When we encounter an obstacle, consciousness returns, deals with the problem, and then fades back into the background. See "System 1" and "System 2" by D. Kahneman.
At the individual level, the conversion of conscious to unconscious is called skill, habit, or intuition. In a family or tribe, it is called tradition. In a society it becomes culture (see A Hunter-Gatherer’s Guide to the 21st Century).
A corporate culture is the same thing: a set of unconscious values and rules that guide people’s behavior.
Much like an individual, a tribe or a company is "unconscious" most of the time. We do things the same way that worked before. When everything is working, we do not all need to get together and discuss every tiny detail.
But when something goes wrong, we become collectively aware. We share the information and ideas that each member is aware of, and then propose hypotheses, observations, and challenges until we arrive at a new answer. In other words we formulate a strategy.
Then we execute, adapt, and refine the strategy. Over time, it becomes more and more automatic, "unconscious," and becomes part of a culture.
So which is more important, a strategy or a culture? Both. In good times, a culture provides cheap and efficient guidance. When the landscape has changed and the old methods no longer work, a new strategy must be developed and implemented.
The bigger question is how to know if current times are good or not.