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/lex/tokenized_buffer_benchmark.cpp

@@ -214,13 +214,13 @@ class LexerBenchHelper {
       : source_(MakeSourceBuffer(text)) {}
 
   auto Lex() -> TokenizedBuffer {
-    DiagnosticConsumer& consumer = NullDiagnosticConsumer();
+    Diagnostics::Consumer& consumer = Diagnostics::NullConsumer();
     return Lex::Lex(value_stores_, source_, consumer);
   }
 
   auto DiagnoseErrors() -> std::string {
     RawStringOstream result;
-    StreamDiagnosticConsumer consumer(&result);
+    Diagnostics::StreamConsumer consumer(&result);
     auto buffer = Lex::Lex(value_stores_, source_, consumer);
     consumer.Flush();
     CARBON_CHECK(buffer.has_errors(),
@@ -234,8 +234,8 @@ class LexerBenchHelper {
   auto MakeSourceBuffer(llvm::StringRef text) -> SourceBuffer {
     CARBON_CHECK(fs_.addFile(filename_, /*ModificationTime=*/0,
                              llvm::MemoryBuffer::getMemBuffer(text)));
-    return std::move(*SourceBuffer::MakeFromFile(fs_, filename_,
-                                                 ConsoleDiagnosticConsumer()));
+    return std::move(*SourceBuffer::MakeFromFile(
+        fs_, filename_, Diagnostics::ConsoleConsumer()));
   }
 
   SharedValueStores value_stores_;