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/driver/compile_subcommand.cpp

@@ -299,8 +299,8 @@ static auto PhaseToString(CompileOptions::Phase phase) -> std::string {
   }
 }
 
-auto CompileSubcommand::ValidateOptions(NoLocDiagnosticEmitter& emitter) const
-    -> bool {
+auto CompileSubcommand::ValidateOptions(
+    Diagnostics::NoLocEmitter& emitter) const -> bool {
   CARBON_DIAGNOSTIC(
       CompilePhaseFlagConflict, Error,
       "requested dumping {0} but compile phase is limited to `{1}`",
@@ -341,7 +341,7 @@ namespace {
 class CompilationUnit {
  public:
   explicit CompilationUnit(DriverEnv& driver_env, const CompileOptions& options,
-                           DiagnosticConsumer* consumer,
+                           Diagnostics::Consumer* consumer,
                            llvm::StringRef input_filename);
 
   // Loads source and lexes it. Returns true on success.
@@ -411,8 +411,8 @@ class CompilationUnit {
   llvm::raw_pwrite_stream* vlog_stream_;
 
   // Diagnostics are sent to consumer_, with optional sorting.
-  std::optional<SortingDiagnosticConsumer> sorting_consumer_;
-  DiagnosticConsumer* consumer_;
+  std::optional<Diagnostics::SortingConsumer> sorting_consumer_;
+  Diagnostics::Consumer* consumer_;
 
   bool success_ = true;
 
@@ -436,7 +436,7 @@ class CompilationUnit {
 
 CompilationUnit::CompilationUnit(DriverEnv& driver_env,
                                  const CompileOptions& options,
-                                 DiagnosticConsumer* consumer,
+                                 Diagnostics::Consumer* consumer,
                                  llvm::StringRef input_filename)
     : driver_env_(&driver_env),
       options_(options),
@@ -445,7 +445,7 @@ CompilationUnit::CompilationUnit(DriverEnv& driver_env,
   if (vlog_stream_ != nullptr || options_.stream_errors) {
     consumer_ = consumer;
   } else {
-    sorting_consumer_ = SortingDiagnosticConsumer(*consumer);
+    sorting_consumer_ = Diagnostics::SortingConsumer(*consumer);
     consumer_ = &*sorting_consumer_;
   }
   if (options_.dump_mem_usage && IncludeInDumps()) {