Is it possible to create custom button with custom functionality?
Yes. It is possible to add your own custom functionality and use it as shortcode.
Example: (add next code to file functions.php)
add_shortcode('woot_custom_button', function() { woot()->include_assets(); return WOOT_HELPER::draw_html_item('a', array( 'href' => 'javascript: woot_helper.call_popup("call_action_custom1",{a:1,b:2,c:"hello",not_paste:1},"asd","Hello World 2020!!"); void(0);', 'title' => '', 'class' => 'woot-btn' ), 'click on this button'); }); add_action('call_action_custom1', function($args, $call_id) { print_r($args); return "It is custom action in functions.php"; }, 10, 2);
Results: button, on click shows popup with data