Auto merge of #126614 - compiler-errors:uplift-next-trait-solver, r=lcnr

Uplift next trait solver to `rustc_next_trait_solver`

🎉

There's so many FIXMEs! Sorry! Ideally this merges with the FIXMEs and we track and squash them over the near future.

Also, this still doesn't build on anything other than rustc. I still need to fix `feature = "nightly"` in `rustc_type_ir`, and remove and fix all the nightly feature usage in the new trait solver (notably: let-chains).

Also, sorry `@lcnr` I know you asked for me to separate the commit where we `mv rustc_trait_selection/solve/... rustc_next_trait_solver/solve/...`, but I had already done all the work by that point. Luckily, `git` understands the file moves so it should still be relatively reviewable.

If this is still very difficult to review, then I can do some rebasing magic to try to separate this out. Please let me know!

r? lcnr