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/client.php

@@ -13,4 +13,4 @@ Route::prefix('game')->middleware(['findretros.redirect', 'vpn.checker'])->group
 
 // Logo generator
 Route::get('/logo-generator', [LogoGeneratorController::class, 'index'])->name('logo-generator.index');
-Route::post('/logo-generator', [LogoGeneratorController::class, 'store'])->name('store.generated-logo');
+Route::post('/logo-generator', [LogoGeneratorController::class, 'store'])->name('store.generated-logo')->middleware('throttle:10,10');