Rollup merge of #125510 - lcnr:change-proof-trees-to-be-shallow, r=compiler-errors

remove proof tree formatting, make em shallow

Debugging via tracing `RUSTC_LOG=rustc_trait_selection::solve=debug` is now imo slightly more readable then the actual proof tree formatter. Removing everything that's not needed for the `analyse` visitor allows us to remove a bunch of code.

I personally believe that we should continue to use tracing over proof trees for debugging:
- it eagerly prints, allowing us to debug ICEs
- the proof tree builder ends up going out of sync with the actual runtime behavior, which is confusing
- using shallow proof trees is a lot more performant as we frequently do not recurse into all nested goals when using an analyse visitor
- this allows us to clean up the implementation and remove some code

r? ```@compiler-errors```

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