Refactor FileDisk system with per-disk unique names and disk assignments UI

Major changes to the file disk subsystem:

- Each FileDisk now gets a unique Laravel disk name (disk_{id}) instead
  of temp_{driver}, fixing the bug where multiple local disks with
  different roots overwrote each other's config.

- Move disk registration logic from FileDisk model to FileDiskService
  (registerDisk, getDiskName). Model keeps only getDecodedCredentials
  and a deprecated setConfig() wrapper.

- Add Disk Assignments admin UI (File Disk tab) with three purpose
  dropdowns: Media Storage, PDF Storage, Backup Storage. Stored as
  settings (media_disk_id, pdf_disk_id, backup_disk_id).

- Backup tab now uses the assigned backup disk instead of a per-backup
  dropdown. BackupsController refactored to use BackupService which
  centralizes disk resolution. Removed stale 4-second cache.

- Add local_public disk to config/filesystems.php so system disks
  are properly defined.

- Local disk roots stored relative to storage/app/ with hint text
  in the admin modal explaining the convention.

- Fix BaseModal watchEffect -> watch to prevent infinite request
  loops on the File Disk page.

- Fix string/number comparison for disk purpose IDs from settings.

- Add safeguards: prevent deleting disks with files, warn on
  purpose change, prevent deleting system disks.

app/Services/Backup/BackupConfigurationFactory.php

@@ -3,6 +3,7 @@
 namespace App\Services\Backup;
 
 use App\Models\FileDisk;
+use App\Services\FileDiskService;
 use Exception;
 use Spatie\Backup\Config\Config;
 
@@ -16,14 +17,10 @@ class BackupConfigurationFactory
 
         $fileDisk = FileDisk::find($data['file_disk_id']);
 
-        $fileDisk->setConfig();
+        $diskName = app(FileDiskService::class)->registerDisk($fileDisk);
 
-        $prefix = env('DYNAMIC_DISK_PREFIX', 'temp_');
+        config(['backup.backup.destination.disks' => [$diskName]]);
 
-        config(['backup.backup.destination.disks' => [$prefix.$fileDisk->driver]]);
-
-        $config = Config::fromArray(config('backup'));
-
-        return $config;
+        return Config::fromArray(config('backup'));
     }
 }