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/diagnostics/mocks.cpp

@@ -4,7 +4,7 @@
 
 #include "toolchain/diagnostics/mocks.h"
 
-namespace Carbon {
+namespace Carbon::Diagnostics {
 
 auto PrintTo(const Diagnostic& diagnostic, std::ostream* os) -> void {
   *os << "Diagnostic{";
@@ -17,21 +17,21 @@ auto PrintTo(const Diagnostic& diagnostic, std::ostream* os) -> void {
   *os << "\"}";
 }
 
-auto PrintTo(DiagnosticLevel level, std::ostream* os) -> void {
+auto PrintTo(Level level, std::ostream* os) -> void {
   switch (level) {
-    case DiagnosticLevel::LocationInfo:
+    case Level::LocationInfo:
       *os << "LocationInfo";
       break;
-    case DiagnosticLevel::Note:
+    case Level::Note:
       *os << "Note";
       break;
-    case DiagnosticLevel::Warning:
+    case Level::Warning:
       *os << "Warning";
       break;
-    case DiagnosticLevel::Error:
+    case Level::Error:
       *os << "Error";
       break;
   }
 }
 
-}  // namespace Carbon
+}  // namespace Carbon::Diagnostics