[clang] [clang-tools-extra] [clang] Trim large(-ish) includes from common headers (PR #216946)

[Chandler Carruth via cfe-commits]

chandlerc wrote:

Merging now so this doesn't get stale, thanks for the reviews all and happy to follow-up on anything needed.

https://github.com/llvm/llvm-project/pull/216946