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/check/pattern_match.cpp

@@ -493,7 +493,7 @@ auto MatchContext::DoEmitPatternMatch(Context& context,
       CARBON_DIAGNOSTIC(TuplePatternSizeDoesntMatchLiteral, Error,
                         "tuple pattern expects {0} element{0:s}, but tuple "
                         "literal has {1}",
-                        IntAsSelect, IntAsSelect);
+                        Diagnostics::IntAsSelect, Diagnostics::IntAsSelect);
       context.emitter().Emit(pattern_loc_id, TuplePatternSizeDoesntMatchLiteral,
                              subpattern_ids.size(), subscrutinee_ids.size());
       return;
@@ -531,7 +531,7 @@ auto MatchContext::EmitPatternMatch(Context& context,
   if (entry.pattern_id == SemIR::ErrorInst::SingletonInstId) {
     return;
   }
-  DiagnosticAnnotationScope annotate_diagnostics(
+  Diagnostics::AnnotationScope annotate_diagnostics(
       &context.emitter(), [&](auto& builder) {
         if (kind_ == MatchKind::Caller) {
           CARBON_DIAGNOSTIC(InCallToFunctionParam, Note,