refactor(autoload): migrate theme classes to Composer PSR-4

Move 288 types from global AKSRT_* + inc/classes manual requires into
namespace AKSRT\{Domain} under src/AKSRT/, wire composer.json psr-4,
and slim bootstrap to helpers/modules/hooks only. Split multi-class
widget/gateway files, update admin contract audit paths, and document
the layout in ADR/README.

src/AKSRT/Core/DBMigrator.php

@@ -0,0 +1,45 @@
+<?php
+/**
+ * @package AKSRT
+ */
+
+namespace AKSRT\Core;
+
+defined('ABSPATH') || exit;
+
+class DBMigrator {
+    use DBMigratorPart2;
+    use DBMigratorPart3;
+
+    /** Current schema version; changing it re-runs dbDelta. */
+    const SCHEMA_VERSION = '1.15.0';
+
+    const OPT_KEY = 'aksrt_db_schema_version';
+
+    /**
+     * Historical flag still readable by older code paths.
+     * Plate CPT is now native when registered; prefer post_type_exists().
+     */
+    const OPT_PLATE_CPT_MIGRATED = 'aksrt_plate_cpt_migrated';
+
+    /**
+     * Register hooks.
+     */
+    public static function init(): void {
+        add_action('after_switch_theme', [self::class, 'maybe_migrate']);
+        add_action('admin_init', [self::class, 'maybe_migrate']);
+    }
+
+    /**
+     * Run table schema upgrade when version mismatches.
+     */
+    public static function maybe_migrate(): void {
+        $current = get_option(self::OPT_KEY, '');
+        if ($current === self::SCHEMA_VERSION) {
+            return;
+        }
+
+        self::run();
+        update_option(self::OPT_KEY, self::SCHEMA_VERSION);
+    }
+}