feat(backend): add machine-readable error codes to ProblemDetails

[fpindej]

Problem

The only TODO in the codebase is in src/frontend/src/routes/(public)/oauth/callback/+page.svelte (line 17):

```
// TODO: Remove this map once the backend returns error codes instead of
// English strings, and use those codes as i18n keys directly.
```

Currently, Result.Failure() produces a human-readable `detail` string in `ProblemDetails` responses. The frontend's OAuth callback has a hardcoded `ERROR_MAP` that maps English error message strings to i18n keys. If any backend error string changes, the frontend silently falls back to a generic message.

Proposed Solution

Add a machine-readable `code` extension field to `ProblemDetails` responses alongside the human-readable `detail`:

```json
{
"type": "https://tools.ietf.org/html/rfc9110#section-15.5.10",
"title": "Conflict",
"status": 409,
"detail": "This external account is already linked to another user.",
"code": "oauth_already_linked"
}
```

The frontend can then use `code` as an i18n key directly, eliminating the brittle string-matching `ERROR_MAP`.

Scope

This is a cross-cutting change:

1. Extend `Result`/`Result` with an optional error code field
2. Include `code` in all `ProblemDetails` responses
3. Update the OAuth callback frontend to use codes instead of string matching
4. Gradually migrate other frontend error handling to use codes

Breaking Changes

This is additive (new field), not breaking. Existing consumers that don't read `code` are unaffected.