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/Console/Commands/MigrateMediaToPrivateDisk.php

@@ -4,6 +4,7 @@ namespace App\Console\Commands;
 
 use App\Models\FileDisk;
 use App\Models\Setting;
+use App\Services\FileDiskService;
 use Illuminate\Console\Command;
 use Illuminate\Support\Facades\DB;
 use Illuminate\Support\Facades\File;
@@ -24,21 +25,8 @@ class MigrateMediaToPrivateDisk extends Command
             return self::FAILURE;
         }
 
-        $prefix = env('DYNAMIC_DISK_PREFIX', 'temp_');
-        $targetDiskName = $prefix.$targetDisk->driver;
-
-        // Register disk config without mutating filesystems.default
-        $credentials = collect(json_decode($targetDisk->credentials));
-        $baseConfig = config('filesystems.disks.'.$targetDisk->driver, []);
-
-        foreach ($baseConfig as $key => $value) {
-            if ($credentials->has($key)) {
-                $baseConfig[$key] = $credentials[$key];
-            }
-        }
-
-        config(['filesystems.disks.'.$targetDiskName => $baseConfig]);
-        $targetRoot = $baseConfig['root'] ?? null;
+        $targetDiskName = app(FileDiskService::class)->registerDisk($targetDisk);
+        $targetRoot = config('filesystems.disks.'.$targetDiskName.'.root');
 
         if (! $targetRoot) {
             $this->error('Could not resolve target disk root path.');