[clang] [clang-tools-extra] [clang][NFC] Refactor `CXXNewExpr::InitializationStyle` (re-land) (PR #71417)

[Vlad Serebrennikov via cfe-commits]

Endilll wrote:

> I'd qualify this as a regression, by looking at that the commit was supposed to be an NFC.
Could you please confirm @Endilll?

I'll leave to @AaronBallman to decide whether this is a functional change, but I can confirm that patch is working as intended, because there is an implicit initialization here `const auto *p = new Derived;`, because `Derived` is a class type.

https://github.com/llvm/llvm-project/pull/71417