feat(vault): pick a notebook vault folder on first run

Phase 0 of the file-based storage plan (docs/plans/
2026-06-24-file-based-storage.md). Foundation only — no editor or
DB change yet.

- VaultService (SharedPreferences): stores the vault root path,
  vaultRootValid() = path set AND directory exists.
- VaultSetupScreen: first-run folder picker (file_picker, Windows).
- main.dart gates HomeScreen behind a valid vault, re-prompting if
  the saved folder is gone.
- Settings: a Vault section to change the folder.

Editors still use SQLite; later phases move annotations into
per-file sidecars under the vault. analyze clean, tests green.

lib/l10n/app_localizations_en.dart

@@ -257,4 +257,48 @@ class AppLocalizationsEn extends AppLocalizations {
 
   @override
   String get close => 'Close';
+
+  @override
+  String get vaultSetupTitle => 'Choose your vault';
+
+  @override
+  String get vaultSetupHeadline => 'Pick a folder for your notebooks';
+
+  @override
+  String get vaultSetupBody =>
+      'BadNote stores your notebooks inside one folder you choose — like an Obsidian vault. Pick a folder you control (e.g. a synced folder) so your notes travel with their files.';
+
+  @override
+  String get vaultChooseFolder => 'Choose folder';
+
+  @override
+  String get vaultMissingTitle => 'Your vault folder is missing';
+
+  @override
+  String get vaultMissingBody =>
+      'The folder you picked can\'t be found (it may have been moved, deleted, or on a drive that\'s unplugged). Relocate it or pick a new one.';
+
+  @override
+  String vaultPickFailed(String error) {
+    return 'Couldn\'t open the folder picker: $error';
+  }
+
+  @override
+  String get vaultNotWritable =>
+      'That folder isn\'t writable. Please choose another.';
+
+  @override
+  String get vaultSection => 'Vault';
+
+  @override
+  String get vaultFolderLabel => 'Vault folder';
+
+  @override
+  String get vaultNoneSelected => 'No folder selected';
+
+  @override
+  String get vaultChangeFolder => 'Change vault folder';
+
+  @override
+  String get vaultUpdated => 'Vault folder updated';
 }