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_stack.cpp

@@ -7,11 +7,10 @@
 #include "llvm/ADT/STLExtras.h"
 #include "toolchain/semantics/semantics_node.h"
 
-namespace Carbon {
+namespace Carbon::Check {
 
-auto SemanticsNodeStack::PrintForStackDump(llvm::raw_ostream& output) const
-    -> void {
-  output << "SemanticsNodeStack:\n";
+auto NodeStack::PrintForStackDump(llvm::raw_ostream& output) const -> void {
+  output << "NodeStack:\n";
   for (auto [i, entry] : llvm::enumerate(stack_)) {
     auto parse_node_kind = parse_tree_->node_kind(entry.parse_node);
     output << "\t" << i << ".\t" << parse_node_kind;
@@ -26,4 +25,4 @@ auto SemanticsNodeStack::PrintForStackDump(llvm::raw_ostream& output) const
   }
 }
 
-}  // namespace Carbon
+}  // namespace Carbon::Check