Split Semantics into Check and SemIR namespaces (#3138)

Splits IR files into SemIR, and logic files into Check. These will be
split into separate directories as part of a later move; the namespaces
are being done first in order to vet the switch, and hopefully make
conflicts a little easier to manage due to the substantial renames.

A lot of this is just automated removal of Semantics prefixes from
names, adding namespace references where needed. A few special-cases
are:

- SemanticsIR -> SemIR::File
- A few things were discussed, like Unit, CompileUnit, or CompiledUnit.
Unit was too vague for chandlerc, and I thought CompileUnit might lead
to incorrect inferences (CompilationUnit would be more precise, but
typically written as SemIR::CompilationUnit which is pretty long). File
seemed to be a short name that we could agree on.
- SemanticsIRFormatter -> SemIR::Formatter
- FormatSemanticsIR -> SemIR::FormatFile
- SemanticsFileTest -> CheckFileTest
- It remains in the Testing namespace, where just "FileTest" might be
too broad a name.
- SemanticsDeclarationNameStack::Context ->
Check::DeclarationNameStack::NameContext
  - This avoids a Check::Context name shadowing.

Changes check_internal.h to include ostream.h to improve finding of
Print/operator<< (otherwise it didn't compile).

This is part of #3070

toolchain/semantics/semantics_handle_if_expression.cpp

@@ -4,10 +4,9 @@
 
 #include "toolchain/semantics/semantics_context.h"
 
-namespace Carbon {
+namespace Carbon::Check {
 
-auto SemanticsHandleIfExpressionIf(SemanticsContext& context,
-                                   ParseTree::Node if_node) -> bool {
+auto HandleIfExpressionIf(Context& context, ParseTree::Node if_node) -> bool {
   auto cond_value_id = context.node_stack().PopExpression();
 
   context.node_stack().Push(if_node);
@@ -26,15 +25,15 @@ auto SemanticsHandleIfExpressionIf(SemanticsContext& context,
   return true;
 }
 
-auto SemanticsHandleIfExpressionThen(SemanticsContext& context,
-                                     ParseTree::Node then_node) -> bool {
+auto HandleIfExpressionThen(Context& context, ParseTree::Node then_node)
+    -> bool {
   context.node_stack().Push(then_node, context.node_block_stack().Pop());
   context.AddCurrentCodeBlockToFunction();
   return true;
 }
 
-auto SemanticsHandleIfExpressionElse(SemanticsContext& context,
-                                     ParseTree::Node else_node) -> bool {
+auto HandleIfExpressionElse(Context& context, ParseTree::Node else_node)
+    -> bool {
   auto else_value_id = context.node_stack().PopExpression();
   auto [then_node, then_end_block_id] =
       context.node_stack().PopWithParseNode<ParseNodeKind::IfExpressionThen>();
@@ -61,4 +60,4 @@ auto SemanticsHandleIfExpressionElse(SemanticsContext& context,
   return true;
 }
 
-}  // namespace Carbon
+}  // namespace Carbon::Check