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.dart

@@ -571,6 +571,84 @@ abstract class AppLocalizations {
   /// In en, this message translates to:
   /// **'Close'**
   String get close;
+
+  /// No description provided for @vaultSetupTitle.
+  ///
+  /// In en, this message translates to:
+  /// **'Choose your vault'**
+  String get vaultSetupTitle;
+
+  /// No description provided for @vaultSetupHeadline.
+  ///
+  /// In en, this message translates to:
+  /// **'Pick a folder for your notebooks'**
+  String get vaultSetupHeadline;
+
+  /// No description provided for @vaultSetupBody.
+  ///
+  /// In en, this message translates to:
+  /// **'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.'**
+  String get vaultSetupBody;
+
+  /// No description provided for @vaultChooseFolder.
+  ///
+  /// In en, this message translates to:
+  /// **'Choose folder'**
+  String get vaultChooseFolder;
+
+  /// No description provided for @vaultMissingTitle.
+  ///
+  /// In en, this message translates to:
+  /// **'Your vault folder is missing'**
+  String get vaultMissingTitle;
+
+  /// No description provided for @vaultMissingBody.
+  ///
+  /// In en, this message translates to:
+  /// **'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.'**
+  String get vaultMissingBody;
+
+  /// No description provided for @vaultPickFailed.
+  ///
+  /// In en, this message translates to:
+  /// **'Couldn\'t open the folder picker: {error}'**
+  String vaultPickFailed(String error);
+
+  /// No description provided for @vaultNotWritable.
+  ///
+  /// In en, this message translates to:
+  /// **'That folder isn\'t writable. Please choose another.'**
+  String get vaultNotWritable;
+
+  /// No description provided for @vaultSection.
+  ///
+  /// In en, this message translates to:
+  /// **'Vault'**
+  String get vaultSection;
+
+  /// No description provided for @vaultFolderLabel.
+  ///
+  /// In en, this message translates to:
+  /// **'Vault folder'**
+  String get vaultFolderLabel;
+
+  /// No description provided for @vaultNoneSelected.
+  ///
+  /// In en, this message translates to:
+  /// **'No folder selected'**
+  String get vaultNoneSelected;
+
+  /// No description provided for @vaultChangeFolder.
+  ///
+  /// In en, this message translates to:
+  /// **'Change vault folder'**
+  String get vaultChangeFolder;
+
+  /// No description provided for @vaultUpdated.
+  ///
+  /// In en, this message translates to:
+  /// **'Vault folder updated'**
+  String get vaultUpdated;
 }
 
 class _AppLocalizationsDelegate