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>

docs/architecture/language-i18n.md

@@ -44,18 +44,20 @@ language = "lux"      # ❌ Use "lb"
 
 ## Language Context Flow
 
-### Resolution Priority
+### Resolution Priority (per Frontend Type)
 
-Language is resolved in this order (highest to lowest priority):
+Language resolution varies by frontend type. Each chain is evaluated top-to-bottom, first match wins:
 
-1. **URL parameter** (`?lang=fr`)
-2. **Cookie** (`orion_language`)
-3. **User preference** (database: `preferred_language`)
-4. **Store default** (database: `storefront_language` or `dashboard_language`)
-5. **Accept-Language header** (browser)
-6. **Platform default** (`fr`)
+| Frontend | Priority (highest → lowest) |
+|----------|----------------------------|
+| **ADMIN** | User `preferred_language` → `"en"` |
+| **STORE** | Cookie (`lang`) → User `preferred_language` → Store `dashboard_language` → `"fr"` |
+| **STOREFRONT** | Customer `preferred_language` → Cookie (`lang`) → Store `storefront_language` → Browser `Accept-Language` → `"fr"` |
+| **PLATFORM** | Cookie (`lang`) → Browser `Accept-Language` → `"fr"` |
 
-### Store Dashboard vs Storefront
+The **cookie** (`lang`) is set by the language switcher UI via `POST /api/v1/platform/language/set` and represents the user's most recent explicit language choice. It takes priority over database preferences because it reflects an immediate UI action.
+
+### Database Fields
 
 | Context | Language Source | Database Field |
 |---------|-----------------|----------------|
@@ -210,7 +212,7 @@ function languageSelector(currentLang, enabledLanguages) {
                 return;
             }
             try {
-                const response = await fetch('/api/v1/language/set', {
+                const response = await fetch('/api/v1/platform/language/set', {
                     method: 'POST',
                     headers: { 'Content-Type': 'application/json' },
                     body: JSON.stringify({ language: lang })
@@ -270,11 +272,12 @@ async def set_language(request: LanguageSetRequest, response: Response):
         raise HTTPException(status_code=400, detail="Unsupported language")
 
     response.set_cookie(
-        key="orion_language",
+        key="lang",
         value=request.language,
         max_age=365 * 24 * 60 * 60,  # 1 year
-        httponly=True,
-        samesite="lax"
+        httponly=False,  # Accessible to JavaScript
+        samesite="lax",
+        path="/",  # Must be site-wide
     )
     return {"success": True, "language": request.language}
 ```
@@ -379,16 +382,16 @@ languageFlags: {
 
 ```javascript
 // ✅ GOOD: Correct endpoint
-fetch('/api/v1/language/set', {
+fetch('/api/v1/platform/language/set', {
     method: 'POST',
     headers: { 'Content-Type': 'application/json' },
     body: JSON.stringify({ language: lang })
 });
 
 // ❌ BAD: Wrong endpoint or method
-fetch('/api/language/set', ...);     // ❌ Missing /v1
-fetch('/api/v1/language', ...);      // ❌ Missing /set
-fetch('/api/v1/language/set', { method: 'GET' });  // ❌ Should be POST
+fetch('/api/v1/language/set', ...);     // ❌ Missing /platform
+fetch('/api/v1/platform/language', ...);      // ❌ Missing /set
+fetch('/api/v1/platform/language/set', { method: 'GET' });  // ❌ Should be POST
 ```
 
 ---
@@ -467,7 +470,7 @@ static/locales/
 - [ ] Provides default values for both parameters
 - [ ] Uses native language names (Français, Deutsch, Lëtzebuergesch)
 - [ ] Uses correct flag codes (en→gb, fr→fr, de→de, lb→lu)
-- [ ] Calls `/api/v1/language/set` with POST method
+- [ ] Calls `/api/v1/platform/language/set` with POST method
 - [ ] Reloads page after successful language change
 - [ ] Hides selector if only one language enabled (storefront)
 - [ ] Shows all languages (store dashboard)
@@ -491,7 +494,7 @@ static/locales/
 | `static/store/js/init-alpine.js` | JS | `languageSelector()` function |
 | `app/templates/shop/base.html` | Template | Storefront language selector |
 | `app/templates/store/partials/header.html` | Template | Dashboard language selector |
-| `app/api/v1/shared/language.py` | API | Language endpoints |
+| `app/modules/core/routes/api/platform.py` | API | Language endpoints (`/api/v1/platform/language/*`) |
 | `middleware/language.py` | Middleware | Language detection |
 | `static/locales/*.json` | JSON | Translation files |