[clang] Reapply "[Clang][Driver] Final phase also determined by input" (PR #225678)

[Fangrui Song via cfe-commits]

MaskRay wrote:

I'm rejecting this reland, and in hindsight #218802 should not have landed either. The O(n^2) is fixed (20k inputs: 0.28s, vs 1.39s with #218802), but the problem is the behavior change itself. https://github.com/llvm/llvm-project/pull/218802#issuecomment-5860940516

https://github.com/llvm/llvm-project/pull/225678