Support

ATS is a Joomla! component. Convert Forms is a Joomla! component. They run on the same site. You do not need an API.

ATS uses the standard Joomla! 4 MVC. Convert Forms allows you to use custom PHP code. You could, therefore, figure out how to post tickets like that. The overall idea is this:

// Get the ATS Ticket and Post tables 
$mvcFactory = \Joomla\CMS\Factory::getApplication()
  ->bootComponent('com_ats')
  ->getMVCFactory();
$ticket = $mvcFactory->createTable('Ticket', 'Administrator');
$post = $mvcFactory->createTable('Post', 'Administrator');

// Create the ticket, telling ATS to ignore the current user's permissions
\Akeeba\Component\ATS\Administrator\Table\TicketTable::$overrideuser = true;
if (!$ticket->save($ticketData)) {
  // You have an error. Handle it.
}
\Akeeba\Component\ATS\Administrator\Table\TicketTable::$overrideuser = false;

// Create the post
$post->ticket_id = $ticket->getId();
$post->created_by = $ticket->created_by;
$post->save($postData);

$ticketData is the PHP array with the ticket data. The keys of the array are the same as the #__ats_tickets table fields. Do not provide a value for the id field; leave it null. If you are submitting a Guest Ticket you MUST provide three additional keys: name, username, and email.

Likewise, $postData is the PHP array with the first post's data for the ticket. They keys of the array are the same as the #__ats_posts table fields. Do not provide a value for the id field; leave it null.

You would of course need to check if there is an existing user logged in, or one which already exists with this email the visitor provided, and use their user ID. You need to figure out how to create the arrays from the form data. These are beyond the scope of what we can help with, but at least you've got a pretty good idea of how to proceed.

You can use this concept even with Akeeba Ticket System Core. You just won't be receiving any emails on ticket submission, but your tickets will be created.