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/Providers/AppConfigProvider.php

@@ -4,6 +4,7 @@ namespace App\Providers;
 
 use App\Models\FileDisk;
 use App\Models\Setting;
+use App\Services\FileDiskService;
 use App\Services\Setup\InstallUtils;
 use Illuminate\Support\Facades\Config;
 use Illuminate\Support\ServiceProvider;
@@ -163,28 +164,16 @@ class AppConfigProvider extends ServiceProvider
     protected function configureFileSystemFromDatabase(): void
     {
         try {
-            // Register the default file disk config without changing filesystems.default.
-            // Calling setConfig() mutates the global default which causes side effects
-            // on pages that make multiple API requests (e.g., File Disk admin page).
             $fileDisk = FileDisk::whereSetAsDefault(true)->first();
 
-            if ($fileDisk) {
-                $prefix = env('DYNAMIC_DISK_PREFIX', 'temp_');
-                $diskName = $prefix.$fileDisk->driver;
-                $credentials = collect(json_decode($fileDisk->credentials));
-                $baseConfig = config('filesystems.disks.'.$fileDisk->driver, []);
-
-                foreach ($baseConfig as $key => $value) {
-                    if ($credentials->has($key)) {
-                        $baseConfig[$key] = $credentials[$key];
-                    }
-                }
-
-                config(['filesystems.disks.'.$diskName => $baseConfig]);
-
-                // Point Spatie Media Library at the same disk
-                config(['media-library.disk_name' => $diskName]);
+            if (! $fileDisk) {
+                return;
             }
+
+            $diskName = app(FileDiskService::class)->registerDisk($fileDisk);
+
+            // Point Spatie Media Library at the resolved disk
+            config(['media-library.disk_name' => $diskName]);
         } catch (\Exception $e) {
             // Silently fail if database is not available (during installation, migrations, etc.)
         }