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`

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