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/string_literal_test.cpp

@@ -16,7 +16,7 @@ namespace {
 
 class StringLiteralTest : public ::testing::Test {
  public:
-  StringLiteralTest() : error_tracker_(ConsoleDiagnosticConsumer()) {}
+  StringLiteralTest() : error_tracker_(Diagnostics::ConsoleConsumer()) {}
 
   auto Lex(llvm::StringRef text) -> StringLiteral {
     std::optional<StringLiteral> result = StringLiteral::Lex(text);
@@ -32,7 +32,7 @@ class StringLiteralTest : public ::testing::Test {
   }
 
   llvm::BumpPtrAllocator allocator_;
-  ErrorTrackingDiagnosticConsumer error_tracker_;
+  Diagnostics::ErrorTrackingConsumer error_tracker_;
 };
 
 TEST_F(StringLiteralTest, StringLiteralBounds) {