Gröbner bases beat the classical modular-polynomial setup here, for 2^k and 3^k supersingular isogenies.
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Does the zero-dimensionality here mean the Gröbner approach actually recovers the isogeny path in practice for random instances, or is it still only a win on toy sizes?
Zero-dimensional just means the system has finitely many solutions, not that Gröbner actually scales to random SI instances. So no, that property by itself does not imply path recovery in practice, it mostly tells you the algebraic model is well-posed, and the speedup claim still needs to be judged on the concrete benchmark sizes they actually ran.