Implement backtracking for multi_phase_search, set max depth for 4x4x4 phase3 solver

[Nogesma]

Switch the SearchPhase trait solutions to not take a mutable reference, and instead use a RefCell to get interior mutability for increasing the size of the prune table.

Also sets the max_depth_exclusive to 15 for the 4x4x4 phase3.
From what I benchmarked, setting it to 14, as it was in the comment makes it take several times longer to solve. Increasing it to 15 fixes it.

This is basically a ~1% regression for scrambles that were finding a solution without backtracking, due to the introduction of the RefCell, but a improvement of 10-35% for the rest. The benchmark code I used is in src/lib/bin/bench4x4x4.rs

[lgarron]

Backtracking for multi-phase is definitely something I've wanted for a while!

Before I take a look, I need to ask: was an LLM or similar tool used in preparing this PR in any way?

[Nogesma]

The code is entirely mine, but I did use an LLM to get better understanding of the repo before I implemented this ie. asking question about the code, but never asking it to write code.

[Nogesma]

After testing a bit more, I noticed some scrambles can take a lot more time (~400s). This is due to the solver not finding a solution at depth 14 for phase3, for multiple phase2 solutions.
I checked how tnoodle handles this, and they actually increase the max depth after a number of failed attempts (100 in their case). And they also seem to store the phase2 results to retry them after increasing the depth.

I was thinking of adding a field to IndividualSearchOptions to handle the increase in max depth.
I think in the case of 4x4, because of the slow phase3, having it increase the depth after 2-3 attempts would yield the best results.
As phase2 is so fast compared to phase3, I don't think storing the result is really needed for now. But maybe restarting the entire phase2 search from the start is required.