[clang] [Clang] [NFC] Move diagnostics emitting code from `DiagnosticIDs` into `DiagnosticsEngine` (PR #143517)

[Mariya Podchishchaeva via cfe-commits]

https://github.com/Fznamznon approved this pull request.

That makes sense to me, but I've never touched that before, so probably makes sense to wait for the feedback from @AaronBallman too.

https://github.com/llvm/llvm-project/pull/143517