Furthermore, various heuristics can speed up the backtracking a lot compared to a brute force approach. As anyone who has implemented a Sudoku solver can attest, a brute force backtracking is easy to implement but will immediately get bogged down with slowness.
e.g. https://www.minizinc.org/ offers a high level modelling language that can target a few different solver backends
might be pretty good results to completely ignore writing a custom algorithm and drop in an existing industrial-grade constraint programming solver, model your procgen problem using a high level language, and use the existing solver to find you random solutions (or exhaustively enumerate them). then more time to iterate on changing the problem definition to produce more interesting maps rather than getting bogged down writing a solver.