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/testing/compile_helper.cpp

@@ -7,7 +7,7 @@
 namespace Carbon::Testing {
 
 auto CompileHelper::GetTokenizedBuffer(llvm::StringRef text,
-                                       DiagnosticConsumer* consumer)
+                                       Diagnostics::Consumer* consumer)
     -> Lex::TokenizedBuffer& {
   auto& source = GetSourceBuffer(text);
 
@@ -18,7 +18,7 @@ auto CompileHelper::GetTokenizedBuffer(llvm::StringRef text,
 }
 
 auto CompileHelper::GetTokenizedBufferWithSharedValueStore(
-    llvm::StringRef text, DiagnosticConsumer* consumer)
+    llvm::StringRef text, Diagnostics::Consumer* consumer)
     -> std::pair<Lex::TokenizedBuffer&, SharedValueStores&> {
   auto& tokens = GetTokenizedBuffer(text, consumer);
   return {tokens, value_store_storage_.front()};