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_codeblock.cpp

@@ -4,20 +4,19 @@
 
 #include "toolchain/semantics/semantics_context.h"
 
-namespace Carbon {
+namespace Carbon::Check {
 
-auto SemanticsHandleCodeBlockStart(SemanticsContext& context,
-                                   ParseTree::Node parse_node) -> bool {
+auto HandleCodeBlockStart(Context& context, ParseTree::Node parse_node)
+    -> bool {
   context.node_stack().Push(parse_node);
   context.PushScope();
   return true;
 }
 
-auto SemanticsHandleCodeBlock(SemanticsContext& context,
-                              ParseTree::Node /*parse_node*/) -> bool {
+auto HandleCodeBlock(Context& context, ParseTree::Node /*parse_node*/) -> bool {
   context.PopScope();
   context.node_stack().PopForSoloParseNode<ParseNodeKind::CodeBlockStart>();
   return true;
 }
 
-}  // namespace Carbon
+}  // namespace Carbon::Check