Here is an example…

 //..path/to/wp-content/plugins/your-plugin-basedir/
 $path  = plugin_dir_path( __FILE__); 

 //..directory within your plugin 
 $path .= 'templates';                

 //..continue with your script...
 $dir_handle = @opendir($path) or die("Cannot open the damn file $path");

UPDATE

I tested the rest of your script by the way, to see if it in fact did read the directory and list files with the *.php extension and it wouldn’t work.

Instead after modifying it to;

$dir_handle = @opendir($path) or die("Cannot open the damn file $path");

while ($file = readdir($dir_handle)) {

    //get length of filename inc. extension
    $length_of_filename = strlen($file); 

    //strip all but last three characters from file name to get extension
    $ext = substr($file, -3, $length_of_filename); 

    if($ext == "php" ) {

    $TheLinkedFile = $path."https://wordpress.stackexchange.com/".$file;

        if(file_exists($TheLinkedFile)) {
            echo $TheLinkedFile.'<br>';
        } else {
            echo "nothing";
        }
    }

}

closedir($dir_handle);

It works…