How to jQuery Ajax show new data from successful insert?

Modify your code as follows:

add_action('wp_ajax_send_projectmessage', 'send_projectmessage');
function send_projectmessage() {
    global $wpdb;
    $wpdb->insert( //insert stuff to db table));

    // Call your function to retrieve your data and send it to browser
    $messages = load_projectmessages($projectid);

    wp_send_json_success($messages);    
}

Display data through JS by modifying this

ajaxRequest.done(function(data) { console.log(data); });

to this

ajaxRequest.done(function(data) { 
    // Put markup for retrieved data here
    // for example 

    var o = "<table><tr><td>Project ID</td><td>Message</td></tr>";

    for (i=0; i<=data.length; i++){
        o .=  "<tr><td>"+data.projectid+"</td><td>"+data.message"+</td></tr>";
    }

    o .=   "</table>";

    $(#messages).html(o); 

 });

Also make sure that your function return an array instead of an OBJECT, so modify it as follows:

function load_projectmessages($projectid) {
    global $wpdb;
    $sql_displaymessages = $wpdb->prepare("sql stuff", $projectid );

    // Add ARRAY_A to get result in an associative array
    $projectmessages = $wpdb->get_results($sql_displaymessages, ARRAY_A);
    return $projectmessages;

    // Not needed
    // wp_die();
}

I hope this will help.

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