fix: language switcher stuck in French on store dashboard

Three compounding bugs prevented language switching on the store dashboard:
- Cookie missing path="/", scoping it to the API endpoint path only
- STORE frontend resolution chain ignored the cookie entirely
- Store header used inline x-data with wrong language names instead of shared languageSelector()

Also updates architecture doc with correct per-frontend resolution priorities,
cookie name, API endpoint path, and file references.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

app/utils/i18n.py

@@ -351,15 +351,20 @@ def get_jinja2_globals(language: str = None) -> dict:
 def resolve_store_dashboard_language(
     user_preferred: str | None,
     store_dashboard: str | None,
+    cookie_language: str | None = None,
 ) -> str:
     """
     Resolve language for store dashboard.
 
     Priority:
-    1. User's preferred_language (if set)
-    2. Store's dashboard_language
-    3. System default (fr)
+    1. Cookie (explicit UI action via language switcher)
+    2. User's preferred_language (DB preference from profile settings)
+    3. Store's dashboard_language
+    4. System default (fr)
     """
+    if cookie_language and cookie_language in SUPPORTED_LANGUAGES:
+        return cookie_language
+
     if user_preferred and user_preferred in SUPPORTED_LANGUAGES:
         return user_preferred