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/parse/handle_brace_expr.cpp

@@ -23,7 +23,7 @@ auto HandleBraceExpr(Context& context) -> void {
 static auto HandleBraceExprParamError(Context& context,
                                       Context::StateStackEntry state,
                                       State param_finish_state) -> void {
-  IntAsSelect mode(0);
+  Diagnostics::IntAsSelect mode(0);
   switch (param_finish_state) {
     case State::BraceExprParamFinishAsType:
       mode.value = 0;
@@ -41,7 +41,7 @@ static auto HandleBraceExprParamError(Context& context,
       ExpectedStructLiteralField, Error,
       "expected {0:=0:`.field: field_type`|"
       "=1:`.field = value`|=2:`.field: field_type` or `.field = value`}",
-      IntAsSelect);
+      Diagnostics::IntAsSelect);
   context.emitter().Emit(*context.position(), ExpectedStructLiteralField, mode);
 
   state.has_error = true;