Overhaul `Diagnostic` and `DiagnosticBuilder`
Implements the first part of https://github.com/rust-lang/compiler-team/issues/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`