feat(app): extract the user slice into i18n, en+ru (CLEAN-37)

[maksymhryzodub-prog]

Implements CLEAN-37 (subtask of CLEAN-33): https://dreamvention.atlassian.net/browse/CLEAN-37

Stacked on #30 — targets feat/CLEAN-33-i18n-strategy, since the LOCALES constant, the sync script and the CI check all live there. GitHub retargets this to main once #30 merges.

The auth screens were fully hardcoded and the slice had no i18n block at all. This adds one, plus en/ru files, and moves all 39 strings out: the form, the marketing panel on the auth layout, and the closed-registration state. A re-scan finds zero hardcoded strings left in the slice.

The interesting part: copy that lives in script

This slice is the reason the ADR has the "script holds keys, not text" rule, and it exercises every shape of it:

• Validation — errors.email = 'account.email_invalid' instead of "Enter a valid email"; the template renders {{ $t(errors.email!) }}.
• State-dependent copy — titleKey, subtitleKey, submitLabelKey are computeds returning keys ("Welcome back" vs "Create your account", "Signing in…" vs "Sign in").
• Failure copy — both providers dropped their hardcoded English fallback. A provider now reports only whether the call failed (failed) and what the server said (errorMessage, English by design per the ADR); the form owns the fallback wording and picks the key by mode.

useI18n() appears nowhere in the slice — templates use the injected $t.

app_name is reused from the common slice rather than redefined: vue-i18n merges slice messages into one global scope, so brand tokens don't need duplicating.

Bug this uncovered

"jane@example.com" breaks the production build. vue-i18n reads a bare @ as a linked-message reference, so the message compiler fails — and CI would not have caught it, because CI runs typecheck / lint / test / i18n:check, not nuxt build.

Fixed on four fronts:

• the placeholder is now the escaped literal jane{'@'}example.com;
• i18n:check reports a bare @ or | on either side (en or ru) — so CI catches it from now on;
• the translator prompt states the rule;
• a model reply that breaks it is rejected before it reaches disk.

Verification

• nuxt typecheck and nuxt build clean; the Russian auth strings appear in the built client chunks.
• i18n:check green across 5 slice/locale pairs, and it was seen failing on the unescaped @ before the fix.
• Translations generated by bun run i18n:sync (40 keys), including localized example data — the name and email placeholders become Иван Иванов / ivan{'@'}example.com.

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