Auto merge of #122385 - lcnr:analyze-obligations-for-infer, r=compiler-errors

`obligations_for_self_ty`: use `ProofTreeVisitor` for nested goals

As always, dealing with proof trees continues to be a hacked together mess. After this PR and #124380 the only remaining blocker for core is https://github.com/rust-lang/trait-system-refactor-initiative/issues/90. There is also a `ProofTreeVisitor` issue causing an ICE when compiling `alloc` which I will handle in a separate PR. This issue likely affects coherence diagnostics more generally.

The core idea is to extend the proof tree visitor to support visiting nested candidates without using a `probe`. We then simply recurse into nested candidates if they are the only potentially applicable candidate for a given goal and check whether the self type matches the expected one.

For that to work, we need to improve `CanonicalState` to also handle unconstrained inference variables created inside of the trait solver. This is done by extending the `var_values` of `CanoncalState` with each fresh inference variables. Furthermore, we also store the state of all inference variables at the end of each probe. When recursing into `InspectCandidates` we then unify the values of all these states.

r? `@compiler-errors`

compiler/rustc_middle/src/traits/solve/inspect.rs

@@ -102,6 +102,7 @@ pub struct Probe<'tcx> {
     /// What happened inside of this probe in chronological order.
     pub steps: Vec<ProbeStep<'tcx>>,
     pub kind: ProbeKind<'tcx>,
+    pub final_state: CanonicalState<'tcx, ()>,
 }
 
 impl Debug for Probe<'_> {