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_variable.cpp

@@ -5,12 +5,12 @@
 #include "toolchain/semantics/semantics_context.h"
 #include "toolchain/semantics/semantics_node.h"
 
-namespace Carbon {
+namespace Carbon::Check {
 
-auto SemanticsHandleVariableDeclaration(SemanticsContext& context,
-                                        ParseTree::Node parse_node) -> bool {
+auto HandleVariableDeclaration(Context& context, ParseTree::Node parse_node)
+    -> bool {
   // Handle the optional initializer.
-  auto expr_node_id = SemanticsNodeId::Invalid;
+  auto expr_node_id = SemIR::NodeId::Invalid;
   bool has_init =
       context.parse_tree().node_kind(context.node_stack().PeekParseNode()) !=
       ParseNodeKind::PatternBinding;
@@ -21,7 +21,7 @@ auto SemanticsHandleVariableDeclaration(SemanticsContext& context,
   }
 
   // Get the storage and add it to name lookup.
-  SemanticsNodeId var_id =
+  SemIR::NodeId var_id =
       context.node_stack().Pop<ParseNodeKind::PatternBinding>();
   auto var = context.semantics_ir().GetNode(var_id);
   auto name_id = var.GetAsVarStorage();
@@ -31,7 +31,7 @@ auto SemanticsHandleVariableDeclaration(SemanticsContext& context,
     auto cast_value_id =
         context.ImplicitAsRequired(parse_node, expr_node_id, var.type_id());
     context.AddNode(
-        SemanticsNode::Assign::Make(parse_node, var_id, cast_value_id));
+        SemIR::Node::Assign::Make(parse_node, var_id, cast_value_id));
   }
 
   context.node_stack()
@@ -40,18 +40,18 @@ auto SemanticsHandleVariableDeclaration(SemanticsContext& context,
   return true;
 }
 
-auto SemanticsHandleVariableIntroducer(SemanticsContext& context,
-                                       ParseTree::Node parse_node) -> bool {
+auto HandleVariableIntroducer(Context& context, ParseTree::Node parse_node)
+    -> bool {
   // No action, just a bracketing node.
   context.node_stack().Push(parse_node);
   return true;
 }
 
-auto SemanticsHandleVariableInitializer(SemanticsContext& context,
-                                        ParseTree::Node parse_node) -> bool {
+auto HandleVariableInitializer(Context& context, ParseTree::Node parse_node)
+    -> bool {
   // No action, just a bracketing node.
   context.node_stack().Push(parse_node);
   return true;
 }
 
-}  // namespace Carbon
+}  // namespace Carbon::Check