PHP 8, AJAX mail form to function.php doesn’t work

This is the cause of your problem:

function true_add_ajaxform(){
    ...
    function set_html_content_type() {
        return 'text/html';
    }

}

You shouldn’t nest function definitions! Move it out of the function like this:

function true_add_ajaxform(){
    ...
}

function set_html_content_type() {
    return 'text/html';
}