Split up C++ diagnostic emitter and factor it out. (#7558)

Split the diagnostic emitter into a separate emitter (regietered with
Clang) and listener (registered with the emitter). The purpose of this
split is to make the Clang emitter not depend on the `Check::Context`,
so that we can use it, and hence the same Clang instance, with multiple
`Check::Context`s. A fallback listener is registered to collect and emit
any diagnostics produced while we don't have a `Check::Context`
registered with the emitter.

Assisted-by: Gemini via Antigravity

toolchain/check/cpp/import.cpp

@@ -96,16 +96,6 @@ auto AddIdentifierName(Context& context, llvm::StringRef name)
   return SemIR::NameId::ForIdentifier(context.identifiers().Add(name));
 }
 
-// Adds the given source location and an `ImportIRInst` referring to it in
-// `ImportIRId::Cpp`.
-static auto AddImportIRInst(SemIR::File& file,
-                            clang::SourceLocation clang_source_loc)
-    -> SemIR::ImportIRInstId {
-  SemIR::ClangSourceLocId clang_source_loc_id =
-      file.clang_source_locs().Add(clang_source_loc);
-  return file.import_ir_insts().Add(SemIR::ImportIRInst(clang_source_loc_id));
-}
-
 // Adds a namespace for the `Cpp` import and returns its `NameScopeId`.
 static auto AddNamespace(Context& context, PackageNameId cpp_package_id,
                          llvm::ArrayRef<Parse::Tree::PackagingNames> imports)