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/source/source_buffer.cpp

@@ -11,7 +11,7 @@
 
 namespace Carbon {
 
-auto SourceBuffer::MakeFromStdin(DiagnosticConsumer& consumer)
+auto SourceBuffer::MakeFromStdin(Diagnostics::Consumer& consumer)
     -> std::optional<SourceBuffer> {
   return MakeFromMemoryBuffer(llvm::MemoryBuffer::getSTDIN(), "<stdin>",
                               /*is_regular_file=*/false, consumer);
@@ -19,9 +19,9 @@ auto SourceBuffer::MakeFromStdin(DiagnosticConsumer& consumer)
 
 auto SourceBuffer::MakeFromFile(llvm::vfs::FileSystem& fs,
                                 llvm::StringRef filename,
-                                DiagnosticConsumer& consumer)
+                                Diagnostics::Consumer& consumer)
     -> std::optional<SourceBuffer> {
-  FileDiagnosticEmitter emitter(&consumer);
+  Diagnostics::FileEmitter emitter(&consumer);
 
   llvm::ErrorOr<std::unique_ptr<llvm::vfs::File>> file =
       fs.openFileForRead(filename);
@@ -53,7 +53,7 @@ auto SourceBuffer::MakeFromFile(llvm::vfs::FileSystem& fs,
 
 auto SourceBuffer::MakeFromStringCopy(llvm::StringRef filename,
                                       llvm::StringRef text,
-                                      DiagnosticConsumer& consumer)
+                                      Diagnostics::Consumer& consumer)
     -> std::optional<SourceBuffer> {
   return MakeFromMemoryBuffer(
       llvm::MemoryBuffer::getMemBufferCopy(text, filename), filename,
@@ -63,8 +63,8 @@ auto SourceBuffer::MakeFromStringCopy(llvm::StringRef filename,
 auto SourceBuffer::MakeFromMemoryBuffer(
     llvm::ErrorOr<std::unique_ptr<llvm::MemoryBuffer>> buffer,
     llvm::StringRef filename, bool is_regular_file,
-    DiagnosticConsumer& consumer) -> std::optional<SourceBuffer> {
-  FileDiagnosticEmitter emitter(&consumer);
+    Diagnostics::Consumer& consumer) -> std::optional<SourceBuffer> {
+  Diagnostics::FileEmitter emitter(&consumer);
 
   if (buffer.getError()) {
     CARBON_DIAGNOSTIC(ErrorReadingFile, Error, "error reading file: {0}",