feat: implement issue #4

Resolves luca/thetool#4
Closes #4

public/api/health.php

@@ -0,0 +1,50 @@
+<?php
+/**
+ * Health Check Endpoint
+ * Returns application health status and database connectivity
+ */
+
+header('Content-Type: application/json');
+
+$health = [
+    'status' => 'ok',
+    'timestamp' => time()
+];
+
+// Check database connection
+$dbConnected = false;
+$dbError = null;
+
+try {
+    $conn = @mysqli_connect(
+        'aide-mariadb',
+        'aide',
+        'aide',
+        'thetool_s13'
+    );
+
+    if ($conn) {
+        $dbConnected = true;
+        mysqli_close($conn);
+    }
+} catch (Exception $e) {
+    $dbError = $e->getMessage();
+}
+
+if ($dbConnected) {
+    $health['db'] = true;
+} else {
+    $health['db'] = false;
+    if ($dbError) {
+        $health['db_error'] = $dbError;
+    }
+}
+
+// Set HTTP status code
+if ($health['db']) {
+    http_response_code(200);
+} else {
+    http_response_code(503); // Service Unavailable
+}
+
+echo json_encode($health);