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> But I rarely see mention of messier problems which consist of overlapping and perhaps hierarchical states.
That's what State Charts were designed for: https://www.inf.ed.ac.uk/teaching/courses/seoc/2005_2006/res...
It's used as the basis for a number of state machine / state chart libraries, for instance XState: https://xstate.js.org/docs/
You can visualise many FSMs automatically - see this project of mine for an example: https://github.com/jbreckmckye/robot3-viz