Auto merge of #120576 - nnethercote:merge-Diagnostic-DiagnosticBuilder, r=davidtwco

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`

compiler/rustc_pattern_analysis/src/errors.rs

@@ -1,4 +1,4 @@
-use rustc_errors::{AddToDiagnostic, Diagnostic, SubdiagnosticMessageOp};
+use rustc_errors::{AddToDiagnostic, DiagnosticBuilder, EmissionGuarantee, SubdiagnosticMessageOp};
 use rustc_macros::{LintDiagnostic, Subdiagnostic};
 use rustc_middle::thir::Pat;
 use rustc_middle::ty::Ty;
@@ -62,7 +62,11 @@ pub struct Overlap<'tcx> {
 }
 
 impl<'tcx> AddToDiagnostic for Overlap<'tcx> {
-    fn add_to_diagnostic_with<F: SubdiagnosticMessageOp>(self, diag: &mut Diagnostic, _: F) {
+    fn add_to_diagnostic_with<G: EmissionGuarantee, F: SubdiagnosticMessageOp<G>>(
+        self,
+        diag: &mut DiagnosticBuilder<'_, G>,
+        _: F,
+    ) {
         let Overlap { span, range } = self;
 
         // FIXME(mejrs) unfortunately `#[derive(LintDiagnostic)]`