fix(types): make system prompt injection noImplicitAny-safe (#12416)

Closes the remaining noImplicitAny gap in global system-prompt injection without changing valid OpenAI or Claude request behaviour: injectSystemPrompt gets a caller-preserving generic type, unknown bodies/message entries/content are narrowed before access, malformed entries are skipped instead of throwing, and request/message/content immutability is preserved.

Validated in a combined worktree with the batch's ready set boarded onto the current tip: parse sweep clean on every changed TypeScript file, typecheck:core clean, check:dashboard-typecheck OK (207 pre-existing errors, all within baseline), check:cycles OK, check-file-size OK, 203/205 focused node tests and 94/94 vitest — the two failures belong to #12427, which is held back.