Move diagnostics into a namespace (#5173)

What this really does is avoids shadowing names, so that we can
comfortable have things like `Check::DiagnosticEmitter` or
`Check::DiagnosticLoc` without shadowing being a concern.

Note, down this path I'm also thinking about:

- Renaming misc DiagnosticConsumer/DiagnosticEmitter classes, possibly
just to DiagnosticConsumer/DiagnosticEmitter (so
`Check::DiagnosticEmitter` instead of `SemIRLocDiagnosticEmitter`).
- Dropping `Diagnostic` from `Emitter::DiagnosticBuilder`.
- But not for `Check::DiagnosticBuilder`, because `Check::Builder` would
be ambiguous.
- Renaming diagnostics/diagnostic_* to drop "diagnostic".

[Discussion about SemIRLoc ->
DiagnosticLoc](https://discord.com/channels/655572317891461132/655578254970716160/1353771570463768698)
reminded me of this (in particular the older [Check::DiagnosticBuilder
discussion](https://discord.com/channels/655572317891461132/655578254970716160/1344363562608627763)),
but I'd only do that rename if there's matching consensus about a path
forward where we keep SemIRLoc, and in a way that it's only ever used
for diagnostics (the divergence from which is at the root of current
LocId discussion).

I'm trying to keep that separate from a namespace addition for clarity.

toolchain/check/import_cpp.cpp

@@ -83,13 +83,15 @@ static auto GenerateAst(Context& context, llvm::StringRef importing_file_path,
     CARBON_DIAGNOSTIC(
         CppInteropParseError, Error,
         "{0} error{0:s} and {1} warning{1:s} in {2} `Cpp` import{2:s}:\n{3}",
-        IntAsSelect, IntAsSelect, IntAsSelect, std::string);
+        Diagnostics::IntAsSelect, Diagnostics::IntAsSelect,
+        Diagnostics::IntAsSelect, std::string);
     context.emitter().Emit(loc, CppInteropParseError, num_errors, num_warnings,
                            num_imports, diagnostics_str);
   } else if (num_warnings > 0) {
     CARBON_DIAGNOSTIC(CppInteropParseWarning, Warning,
                       "{0} warning{0:s} in `Cpp` {1} import{1:s}:\n{2}",
-                      IntAsSelect, IntAsSelect, std::string);
+                      Diagnostics::IntAsSelect, Diagnostics::IntAsSelect,
+                      std::string);
     context.emitter().Emit(loc, CppInteropParseWarning, num_warnings,
                            num_imports, diagnostics_str);
   }
@@ -348,7 +350,7 @@ static auto ImportNameDecl(Context& context, SemIR::LocId loc_id,
 auto ImportNameFromCpp(Context& context, SemIR::LocId loc_id,
                        SemIR::NameScopeId scope_id, SemIR::NameId name_id)
     -> SemIR::InstId {
-  DiagnosticAnnotationScope annotate_diagnostics(
+  Diagnostics::AnnotationScope annotate_diagnostics(
       &context.emitter(), [&](auto& builder) {
         CARBON_DIAGNOSTIC(InCppNameLookup, Note,
                           "in `Cpp` name lookup for `{0}`", SemIR::NameId);