Does mystified math lie beyond behind how the ratio of input and output voltages is equal to the ratio of the primary and secondary windings? Can it be derived from Maxwell's equations?
Not really mystified in any sense of the word but for more precise calculations of circuit diagrams with transformers you can formulate a system of coupled ODEs which can be written in matrix form leading to the very nice mathematics of matrix differential equations.
I seen an LLM, or maybe another variant of “AI” [0] a while back that could aid design of electronic circuits by having a pool of data sheets added for referencing.
As you were querying specs for a board at component level it could give you a schematic, I think, with citations to the actual data sheets.
I suppose the same scale up could be used for systems that needed a varying number of specific power supplies.
Off to a search...