Initialize cpp_mangle_context_ in Mangler's constructor (#5095)

This is a followup of [a
comment](https://github.com/carbon-language/carbon-lang/pull/5062/files/89e56d51858bcc18d4242d4e5c9ee0e7496d887e#r1979993815)
in #5062.

Add a mutable AST pointer to `FileContext`.

This is necessary since we use [Clang with lack of const
correctness](https://github.com/llvm/llvm-project/pull/130096#issuecomment-2704413782).

Alternatives in Clang:
* Change `ASTUnit::getASTContext() const` to return a non-const
`ASTContext`. [Tried and was rejected upstream due to weakening const
correctness](https://github.com/llvm/llvm-project/pull/130096).
* Change `createMangleContext()` to be `const`. Tried that and it seems
like it relies heavily on non const API.
* Change `MangleContext::mangleName()` to `const`. Tried that but there
are several lazy initialization and id creations happening that modify
the context. See details in
https://github.com/llvm/llvm-project/pull/130613.

Alternatives in Carbon:
* Use `const_cast` on `ASTContext` when calling `createMangleContext()`.
* Make `FileContext::sem_ir_` point to a mutable `SemIR::File`.
* Change `File::cpp_ast()` to be const while keeping it return a mutable
pointer.

Part of #4666.

toolchain/driver/compile_subcommand.cpp

@@ -598,9 +598,10 @@ auto CompilationUnit::RunLower(
     // TODO: Consider disabling instruction naming by default if we're not
     // producing textual LLVM IR.
     SemIR::InstNamer inst_namer(&*sem_ir_);
-    module_ = Lower::LowerToLLVM(
-        *llvm_context_, tree_and_subtrees_getters_for_debug_info,
-        input_filename_, *sem_ir_, &inst_namer, vlog_stream_);
+    module_ = Lower::LowerToLLVM(*llvm_context_,
+                                 tree_and_subtrees_getters_for_debug_info,
+                                 input_filename_, *sem_ir_, sem_ir_->cpp_ast(),
+                                 &inst_namer, vlog_stream_);
   });
   if (vlog_stream_) {
     CARBON_VLOG("*** llvm::Module ***\n");