Fix 40+ codebase issues: security, performance, duplication, dead code, and routes

HIGH:
- Add missing import RadioSongRequestFormRequest (fixes crash on POST)
- Add Purify XSS sanitization for article full_story
- Fix duplicate radio API routes (/api/radio vs /api/radio/v2)
- Add try-catch guards in InstallationController for missing records

MEDIUM:
- Fix N+1: eager load comments.user in ArticleController::show()
- Fix GuestbookController authorization logic
- Remove dead doSetup() method and duplicate route
- Extract shared HasRadioDefaults trait (remove code duplication)
- Use named routes in ForceStaffTwoFactorMiddleware
- Fix WebsiteHelpCenterTicket::isOpen() (no permission leak)
- Enable  on WebsiteHelpCenterTicket (matches schema)
- Replace WebsiteTeam::all()->pluck() with direct pluck()
- Replace CatalogPage::all()->pluck() with direct pluck()
- Replace WebsiteBadge::all() with direct pluck()
- Add throttle middleware to guestbook store, logo-generator, radio embed

LOW:
- Remove unused imports
- Remove dead /inertia-test route
- Consolidate cache keys in RadioController

app/Models/Help/WebsiteHelpCenterTicket.php

@@ -42,7 +42,7 @@ class WebsiteHelpCenterTicket extends Model
     protected $guarded = ['id', 'created_at', 'updated_at', 'user_id', 'status', 'subject', 'category_id'];
 
     #[\Override]
-    public $timestamps = false;
+    public $timestamps = true;
 
     public function category(): BelongsTo
     {
@@ -71,7 +71,7 @@ class WebsiteHelpCenterTicket extends Model
 
     public function isOpen()
     {
-        return $this->open || hasPermission('manage_website_tickets');
+        return (bool) $this->open;
     }
 
     public function getContentAttribute($value)