[clang] [Parse] Remove ParseDiagnostic.h (PR #116496)

[Aaron Ballman via cfe-commits]

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

LGTM! I believe the intent after d076608d58d1ec55016eb747a995511e3a3f72aa was that consumers would eventually be updated to refer to the header in `Basic` rather than in `Parse`, this just completes that.

https://github.com/llvm/llvm-project/pull/116496