Auto merge of #120576 - nnethercote:merge-Diagnostic-DiagnosticBuilde…

…r, r=davidtwco

Overhaul `Diagnostic` and `DiagnosticBuilder`

Implements the first part of rust-lang/compiler-team#722, which moves functionality and use away from `Diagnostic`, onto `DiagnosticBuilder`.

Likely follow-ups:
- Move things around, because this PR was written to minimize diff size, so some things end up in sub-optimal places. E.g. `DiagnosticBuilder` has impls in both `diagnostic.rs` and `diagnostic_builder.rs`.
- Rename `Diagnostic` as `DiagInner` and `DiagnosticBuilder` as `Diag`.

r? `@davidtwco`