Type Safety Documentation Audit & Update

Audit every file in _docs/type/ against the live codebase and fix any errors, gaps, or stale information so the docs are the authoritative single source of truth for the 7-layer type safety chain.

Type Safety Chain: Error Check and Fix (reference)

When running or documenting validation, use this workflow. Full detail lives in _docs/type/TYPE_SAFETY.md (Error Fixing Protocol).

Run error check

1. Full chain: npx tsc --noEmit -p tsconfig.build.json — checks all layers (server + client + shared schema).
2. Client only: npx tsc --noEmit (uses tsconfig.json, covers src/ only).
3. Exit 0 = success (no type errors). Non-zero = failure with errors printed to stdout.

Fix errors (until 0 errors)