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.

resources/scripts-v2/features/admin/components/settings/AdminFileDiskModal.vue

@@ -20,6 +20,7 @@ interface DiskField {
   key: string
   labelKey: string
   placeholder?: string
+  hint?: string
 }
 
 interface DiskDriverOption {
@@ -39,7 +40,8 @@ const DRIVER_FIELDS: Record<DiskDriverValue, DiskField[]> = {
     {
       key: 'root',
       labelKey: 'settings.disk.local_root',
-      placeholder: 'Ex. /user/root/',
+      placeholder: 'Ex. backups',
+      hint: 'settings.disk.local_root_hint',
     },
   ],
   s3: [
@@ -512,6 +514,9 @@ function isDisk(value: unknown): value is Disk {
               :placeholder="field.placeholder"
               @input="touchCredential(field.key)"
             />
+            <span v-if="field.hint" class="text-xs text-subtle mt-1 block">
+              {{ $t(field.hint) }}
+            </span>
           </BaseInputGroup>
         </BaseInputGrid>