Of course you can. Akeeba SocialLogin simply uses Joomla 4's additional login buttons feature. This is a feature I had contributed myself about 5 years ago, to end the awkward tendency of every login method developer that doesn't rely on just a username and password to invent our own hack-ish method to show our login buttons. Now there is a standard in core Joomla.
All you have to do as a login form developer to consume this API is to use Joomla's helper static method, \Joomla\CMS\Helper\AuthenticationHelper::getLoginButtons() and render its results. Do remember to pass your login form's id attribute value as the sole parameter to this helper method; it's required for additional login buttons to work properly.
You can see how to render the results in modules/mod_login/tmpl/default.php, namely the block that starts with <?php foreach ($extraButtons as $button) :. The $extraButtons variable is simply the result of calling the helper method.
Nicholas K. Dionysopoulos
Lead Developer and Director
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