Perform Clang IRGen during check (#6569)

Background:
https://docs.google.com/document/d/1wi85FRiWh4X9A-gCYMVGKR40-q5fM6-3JaSpePk-XCY/edit?usp=sharing
And specifically this work is essentially an alternative to #5543

Clang's code generation is implemented through an ASTListener
(clang::CodeGenerator) that is attached throughout Clang's
parsing/sema/code
generation phases and acts on Clang AST incrementally throughout that
process.

Prior to this patch, Carbon has only created the CodeGenerator during
Carbon's
`lower` phase, missing out on key callbacks that would be made by Clang
during
`check`. Some of these issues were addressed by #6237 and #6483 - but
there were
still remaining cases where the delayed processing lead to missing
functionality.

With #6483 much of the Clang code that made multithreaded complexity of
#5543 is
no longer present, and we have access to the point of ASTListener
registration
so we can register the CodeGenerator there and consume its resulting
llvm::Module during lower.

Examples of some of the bugs this addresses are seen in the linked doc,
and
checked in as tests in this change in
`clang_code_generator_callbacks.carbon`

An indicental bug that's also fixed, and caused all the other test case
churn,
is that the `CodeGenerator` created during `lower` wasn't getting passed
the
Clang `CodeGenOpts` and was creating its own default - so, most notably,
optimization flags were not respected. This meant that the LLVM IR from
Clang
was always -O0 style IR (optnone, no inlinehint, no TBAA, etc). With
this
change, now the Clang IRGen gets the real `CodeGenOpts` and respects
optimization/other flags specified there.

This is only meant to be a rough proof of concept - I'm totally open to
reworking this in any way (even quite substantially) if folks have ideas
about
how this should be implemented most generally/elegantly/etc.

toolchain/check/cpp/import.cpp

@@ -116,6 +116,7 @@ static auto AddNamespace(Context& context, PackageNameId cpp_package_id,
 auto ImportCpp(Context& context,
                llvm::ArrayRef<Parse::Tree::PackagingNames> imports,
                llvm::IntrusiveRefCntPtr<llvm::vfs::FileSystem> fs,
+               llvm::LLVMContext* llvm_context,
                std::shared_ptr<clang::CompilerInvocation> invocation) -> void {
   if (imports.empty()) {
     // TODO: Consider always having a (non-null) AST even if there are no Cpp
@@ -131,7 +132,7 @@ auto ImportCpp(Context& context,
   auto name_scope_id = AddNamespace(context, package_id, imports);
 
   bool ast_has_error =
-      !GenerateAst(context, imports, fs, std::move(invocation));
+      !GenerateAst(context, imports, fs, llvm_context, std::move(invocation));
 
   SemIR::NameScope& name_scope = context.name_scopes().Get(name_scope_id);
   name_scope.set_is_closed_import(true);