Rework "long type names" printing logic

Make it so more type-system types can be printed in a shortened version (like `Predicate`s).

Centralize printing the information about the "full type name path".

Make the "long type path" for the file where long types are written part of `Diag`, so that it becomes easier to keep track of it, and ensure it will always will be printed out last in the diagnostic by making its addition to the output implicit.

Tweak the shortening of types in "expected/found" labels.

Remove dead file `note.rs`.

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