Auto merge of #119735 - lcnr:provisional-cache-readd, r=compiler-errors

next solver: provisional cache

this adds the cache removed in #115843. However, it should now correctly track whether a provisional result depends on an inductive or coinductive stack.

While working on this, I was using the following doc: https://hackmd.io/VsQPjW3wSTGUSlmgwrDKOA. I don't think it's too helpful to understanding this, but am somewhat hopeful that the inline comments are more useful.

There are quite a few future perf improvements here. Given that this is already very involved I don't believe it is worth it (for now). While working on this PR one of my few attempts to significantly improve perf ended up being unsound again because I was not careful enough ✨

r? `@compiler-errors`