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/BackupService.php

@@ -0,0 +1,52 @@
+<?php
+
+namespace App\Services\Backup;
+
+use App\Models\FileDisk;
+use App\Models\Setting;
+use App\Services\FileDiskService;
+use Spatie\Backup\BackupDestination\BackupDestination;
+
+class BackupService
+{
+    public function __construct(
+        private readonly FileDiskService $fileDiskService,
+    ) {}
+
+    /**
+     * Resolve the backup FileDisk from the given ID, settings, or default.
+     */
+    public function resolveBackupDisk(?int $fileDiskId = null): ?FileDisk
+    {
+        if ($fileDiskId) {
+            $disk = FileDisk::find($fileDiskId);
+            if ($disk) {
+                return $disk;
+            }
+        }
+
+        $backupDiskId = Setting::getSetting('backup_disk_id');
+        if ($backupDiskId) {
+            $disk = FileDisk::find($backupDiskId);
+            if ($disk) {
+                return $disk;
+            }
+        }
+
+        return FileDisk::where('set_as_default', true)->first();
+    }
+
+    /**
+     * Create a BackupDestination pointing at the resolved disk.
+     */
+    public function getDestination(?int $fileDiskId = null): BackupDestination
+    {
+        $disk = $this->resolveBackupDisk($fileDiskId);
+
+        $diskName = $disk
+            ? $this->fileDiskService->registerDisk($disk)
+            : config('filesystems.default');
+
+        return BackupDestination::create($diskName, config('backup.backup.name'));
+    }
+}