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

routes/user.php

@@ -21,7 +21,7 @@ Route::prefix('user')->group(function () {
     });
 
     // Guestbook
-    Route::post('/profile/{user}/guestbook', [GuestbookController::class, 'store'])->name('guestbook.store');
+    Route::post('/profile/{user}/guestbook', [GuestbookController::class, 'store'])->name('guestbook.store')->middleware('throttle:5,1');
     Route::delete('/profile/{user}/{guestbook}/delete', [GuestbookController::class, 'destroy'])->name('guestbook.destroy');
 
     // Settings