refactor(utils): group utils/ files into topic folders (Phase L, part 1) (#689)

111 of 122 top-level src/utils/ files move into 16 topic folders (audio,
cache, cover, share, server, playback, playlist, deviceSync, waveform,
mix, format, export, changelog, ui, perf, componentHelpers). True
singletons with no cluster stay at the utils/ root.

Pure file-move: a path-aware codemod rewrote 539 relative-import
specifiers across 275 files; no logic touched. The hot-path coverage
gate list (.github/frontend-hot-path-files.txt) is updated to the new
paths for the 11 gated utils files — a mechanical consequence of the
move, not a CI change. tsc is green.

src/utils/export/backup.ts

@@ -0,0 +1,74 @@
+import { save, open as openDialog } from '@tauri-apps/plugin-dialog';
+import { writeFile, readTextFile } from '@tauri-apps/plugin-fs';
+import { version as appVersion } from '../../../package.json';
+
+const BACKUP_VERSION = 1;
+
+const BACKUP_KEYS = [
+  'psysonic-auth',
+  'psysonic_theme',
+  'psysonic_font',
+  'psysonic_language',
+  'psysonic_keybindings',
+  'psysonic_sidebar',
+  'psysonic-eq',
+  'psysonic_global_shortcuts',
+  'psysonic-player',
+  'psysonic_home',
+];
+
+export async function exportBackup(): Promise<string | null> {
+  const stores: Record<string, unknown> = {};
+  for (const key of BACKUP_KEYS) {
+    const val = localStorage.getItem(key);
+    if (val !== null) {
+      try {
+        stores[key] = JSON.parse(val);
+      } catch {
+        stores[key] = val;
+      }
+    }
+  }
+
+  const manifest = {
+    version: BACKUP_VERSION,
+    app_version: appVersion,
+    created_at: new Date().toISOString(),
+    stores,
+  };
+
+  const today = new Date().toISOString().slice(0, 10);
+  const path = await save({
+    filters: [{ name: 'Psysonic Backup', extensions: ['psybkp'] }],
+    defaultPath: `psysonic-backup-${today}.psybkp`,
+  });
+
+  if (!path) return null;
+
+  const content = JSON.stringify(manifest, null, 2);
+  await writeFile(path, new TextEncoder().encode(content));
+  return path;
+}
+
+export async function importBackup(): Promise<void> {
+  const path = await openDialog({
+    filters: [{ name: 'Psysonic Backup', extensions: ['psybkp'] }],
+    multiple: false,
+    title: 'Import Psysonic Backup',
+  });
+
+  if (!path || typeof path !== 'string') return;
+
+  const raw = await readTextFile(path);
+  const manifest = JSON.parse(raw);
+
+  if (typeof manifest.version !== 'number' || !manifest.stores || typeof manifest.stores !== 'object') {
+    throw new Error('invalid_backup');
+  }
+
+  for (const [key, value] of Object.entries(manifest.stores)) {
+    localStorage.setItem(key, JSON.stringify(value));
+  }
+
+  window.location.reload();
+}