> This is not about implementing a Sudoku solver

If you can capture validity of the game state in the type system, a sufficiently advanced IDE with autocomplete/intellisense could actually already be a naive solver, since they will tend to treat contextual autocomplete as a form of constraint satisfiability problem, which is a sufficient approach to solve easy Sudokus.

In other words, throw this into Webstorm, put your cursor in an empty cell that currently has only one possible answer, and hit ctrl-space, and I would expect it to automatically fill in the answer for you.