as discussed, i see a few corrections are needed:

1. you should call the 'test_testmodule/index/test' url as you defined your frontName as 'test_testmodule'
2. you should use the 'standard' routerId if you are working on the frontend side with this call
3. you are expecting a JSON formatted response as per your AJAX call definition, so you will have to format it serverside by injecting Magento\Framework\Controller\Result\JsonFactory into a protected property (say $resultJsonFactory) inside your controller class and using it like so:

$result = $this->resultJsonFactory->create();
return $result->setData(['success' => true]);

as discussed, i see that a few corrections are needed:

1. you should call the 'test_testmodule/index/test' url as you defined your frontName as 'test_testmodule'
2. you should use the 'standard' routerId if you are working on the frontend side with this call
3. you are expecting a JSON formatted response as per your AJAX call definition, so you will have to format it serverside by injecting Magento\Framework\Controller\Result\JsonFactory into a protected property (say $resultJsonFactory) inside your controller class and using it like so:

$result = $this->resultJsonFactory->create();
return $result->setData(['success' => true]);