Design Thinking (and more broadly, human-centered design) is a pragmatic framework for doing product design in an effective and productive manner. Systems Thinking is a massively more general superset. I'm not really sure how you'd operationalize that on a design project, except by following first principles, which would essentially get you to DT / HCD.
That is exactly the point.
Taking a theory (Systems Thinking), a mental model which has the primary goal of holistically identifying, describing, and understanding wholes and reducing it down to a set of methods/framework out of ease of use (the pragmatism) is exactly the wrong approach in my opinion.
Systems Thinking and all of its applications scenarios are based on epistemology. To turn it into a recipe is a wrongdoing. The whole notion is that one size does not fit all.
The operationalization of Systems Theory for a given case at hand is the responsibility and the transfer function of the operator whose approach this is. The process itself yields understanding and should not be abbreviated.