feat: rename mokojoombackup → mokosuitebackup, add [HOME] placeholder for backup directory

Renames all sub-extensions from mokojoombackup to mokosuitebackup
(package, component, 7 plugins, language files, manifests).

Adds [HOME] placeholder to BackupDirectory and PlaceholderResolver
so users can set backup_dir to [HOME]/backups (outside web root).
Fixes folder browser "access denied" on PHP-FPM shared hosting
where getenv('HOME') returns empty by adding POSIX and JPATH_ROOT
fallback detection.

source/packages/com_mokosuitebackup/api/src/Controller/BackupsController.php

@@ -0,0 +1,100 @@
+<?php
+
+/**
+ * @package     MokoSuiteBackup
+ * @subpackage  com_mokosuitebackup
+ * @author      Moko Consulting <hello@mokoconsulting.tech>
+ * @copyright   Copyright (C) 2026 Moko Consulting. All rights reserved.
+ * @license     GNU General Public License version 3 or later; see LICENSE
+ */
+
+namespace Joomla\Component\MokoSuiteBackup\Api\Controller;
+
+defined('_JEXEC') or die;
+
+use Joomla\CMS\MVC\Controller\ApiController;
+use Joomla\Component\MokoSuiteBackup\Administrator\Engine\BackupEngine;
+
+class BackupsController extends ApiController
+{
+	protected $contentType = 'backups';
+	protected $default_view = 'backups';
+
+	/**
+	 * Start a new backup (POST /api/index.php/v1/mokosuitebackup/backup)
+	 */
+	public function backup(): static
+	{
+		$data = json_decode($this->input->json->getRaw(), true) ?: [];
+
+		$profileId   = (int) ($data['profile'] ?? 1);
+		$description = $data['description'] ?? 'API backup ' . date('Y-m-d H:i:s');
+
+		$engine = new BackupEngine();
+		$result = $engine->run($profileId, $description, 'api');
+
+		if ($result['success']) {
+			$this->app->setHeader('status', 200);
+			echo json_encode(['data' => $result]);
+		} else {
+			$this->app->setHeader('status', 500);
+			echo json_encode(['errors' => [['title' => $result['message']]]]);
+		}
+
+		$this->app->close();
+
+		return $this;
+	}
+
+	/**
+	 * Download a backup archive (GET /api/index.php/v1/mokosuitebackup/backup/:id/download)
+	 */
+	public function download(): static
+	{
+		$id = $this->input->getInt('id', 0);
+
+		$model = $this->getModel('Backup', 'Administrator');
+		$item  = $model->getItem($id);
+
+		if (!$item || !$item->id || !$item->filesexist || !is_file($item->absolute_path)) {
+			$this->app->setHeader('status', 404);
+			echo json_encode(['errors' => [['title' => 'Backup file not found']]]);
+			$this->app->close();
+
+			return $this;
+		}
+
+		$content = base64_encode(file_get_contents($item->absolute_path));
+
+		$this->app->setHeader('status', 200);
+		echo json_encode(['data' => $content]);
+		$this->app->close();
+
+		return $this;
+	}
+
+	/**
+	 * List backup profiles (GET /api/index.php/v1/mokosuitebackup/profiles)
+	 */
+	public function profiles(): static
+	{
+		$model = $this->getModel('Profiles', 'Administrator');
+		$items = $model->getItems();
+
+		$data = [];
+
+		foreach ($items as $item) {
+			$data[] = [
+				'type'       => 'profiles',
+				'id'         => $item->id,
+				'attributes' => $item,
+			];
+		}
+
+		$this->app->setHeader('status', 200);
+		echo json_encode(['data' => $data]);
+		$this->app->close();
+
+		return $this;
+	}
+}