Thread the API error `code` through to typed `AppError`s (replaces string-sniffing)

[Adron]

Discovered while implementing #33, and it affects every feature module — filing it rather than
smuggling a repo-wide refactor into an unrelated PR.

The problem

Every InterlinedList API error comes back as:

{ "error": "<human message>", "code": "<snake_case_code>" }

The app throws the code away. ErrorDto in :core:network models only { "error": ... }, and
safeApiCall maps HTTP status → AppError, with the AppError subclasses in :core:common
carrying just a message.

Two concrete costs:

1. Distinct failures collapse. :feature:ai had to define its own module-local
   AiError/AiResult (see AI: status, gating and quota plumbing (:feature:ai scaffold) #4 / PR feat(ai): :feature:ai scaffold — status, gating, quota and preview→confirm (#4) #92) purely because the shared AppError cannot tell
   quota_exceeded from rate_limited — both are HTTP 429 — nor no_provider_configured from a
   generic conflict. Every future module with meaningful error codes will face the same fork.
2. safeApiCall currently string-sniffs. It decides SubscriptionRequired with a
   message.contains("subscription") heuristic. That is a user-visible behaviour hanging off
   English prose in a server response — it breaks the day the copy is reworded.

What to do

• Add code to ErrorDto.
• Widen AppError (or add a typed code alongside the message) so call sites can branch on the
  server's own vocabulary.
• Replace the contains("subscription") heuristic with the real code.
• Fold :feature:ai's module-local AiError back onto the shared type once it can express
  quota_exceeded / rate_limited (+ Retry-After) / no_provider_configured.

Why it is filed rather than done

It touches every AppError construction site across all feature modules, so it needs a quiet
moment with no parallel branches in flight — otherwise it conflicts with everything. Best done
after the current parity wave merges.

Observed codes so far: bad_request (rejected viewingPreference), unauthorized
(GET /api/auth/accounts to a bearer token), plus quota_exceeded, rate_limited and
no_provider_configured documented at https://interlinedlist.com/help/api/ai-integration.