God's algorithm is not computationally feasible on consumer hardware so I'd assume not although there are many algorithms that can get pretty close (either matching or 1-2 moves off the optimal solution) which are much faster to solve. If you're curious, look up Cube Explorer which is an app that's built for this.

God's algorithm has worked fine on consumer hardware for decades. Look up Korf. Even Cube Explorer has an optimal solver.

Not in practice. Computing the absolute minimum solution for every possible position is computationally infeasible for a web-based solver. This uses Kociemba’s two-phase algorithm instead, which produces very efficient solutions, usually close to optimal, without requiring enormous amounts of time and memory.

Why infeasible? cube20.org says "a good desktop PC" can optimally solve 0.36 random positions per second. And that's from the year 2010. I don't see why a web-based solver 16 years later should be much slower.

And apparently vcube optimally solved six cubes per second eight years ago already: https://github.com/Voltara/vcube