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_node.cpp

@@ -4,10 +4,10 @@
 
 #include "toolchain/semantics/semantics_node.h"
 
-namespace Carbon {
+namespace Carbon::SemIR {
 
 static auto PrintArgs(llvm::raw_ostream& /*out*/,
-                      const SemanticsNode::NoArgs /*no_args*/) -> void {}
+                      const Node::NoArgs /*no_args*/) -> void {}
 
 template <typename T>
 static auto PrintArgs(llvm::raw_ostream& out, T arg) -> void {
@@ -20,19 +20,21 @@ static auto PrintArgs(llvm::raw_ostream& out, std::pair<T0, T1> args) -> void {
   out << ", arg1: " << args.second;
 }
 
-auto SemanticsNode::Print(llvm::raw_ostream& out) const -> void {
-  out << "{kind: " << kind_;
-  switch (kind_) {
+auto operator<<(llvm::raw_ostream& out, const Node& node)
+    -> llvm::raw_ostream& {
+  out << "{kind: " << node.kind_;
+  switch (node.kind_) {
 #define CARBON_SEMANTICS_NODE_KIND(Name) \
-  case SemanticsNodeKind::Name:          \
-    PrintArgs(out, GetAs##Name());       \
+  case NodeKind::Name:                   \
+    PrintArgs(out, node.GetAs##Name());  \
     break;
 #include "toolchain/semantics/semantics_node_kind.def"
   }
-  if (type_id_.is_valid()) {
-    out << ", type: " << type_id_;
+  if (node.type_id_.is_valid()) {
+    out << ", type: " << node.type_id_;
   }
   out << "}";
+  return out;
 }
 
-}  // namespace Carbon
+}  // namespace Carbon::SemIR