[clang] [clang] Apply internal buffering to clang diagnostics printing (PR #113440)

[Mariya Podchishchaeva via cfe-commits]

Fznamznon wrote:

Ping? Does that make sense? If so, I'll try to figure clangd output swap that caused lit fail (which seems harmless).
If not, I'll abandon this.

https://github.com/llvm/llvm-project/pull/113440