I've found a solution using Ajax with native Javascript as follows:

// Filename send2server.js
const sendToServer = function() {
   /* Prepare the object to be sent: ********************************************************************/
   var params = new FormData();
   params.append('action',   'update_sql');                // update_sql is implemented in PHP (see below)
   params.append('quoteAtt', props.attributes.quoteAtt);   // Implemented in PHP

   /* Create the Ajax connection object: ****************************************************************/
   var request = new XMLHttpRequest();
   request.open('POST', ajax_object.ajax_url, true);       // ajax_object.ajax_url defined in PHP (below)
   request.send(params);                                   // Send request to server
}

On the server side, the following functions receive the request in the following manner:

// File plugin.php
function load_ajax_script() {
    wp_enqueue_script(
        'send2server',
        plugins_url( 'send2server.js', __FILE__ ),
        array(),
        filemtime( plugin_dir_path( __FILE__ ) . 'send2server.js' )
    );

    wp_localize_script(                                // make ajaxurl available to Javascript
        'send2server', 
        'ajax_object', 
        array( 'ajax_url' => admin_url( 'admin-ajax.php' ) ) 
    );  
}
add_action('init', 'load_ajax_script');


function update_sql() {                                // Invoked by request.send()
    $received = $_POST["quoteAtt"];                    // Contents of quoteAtt
    // ...
}
add_action('wp_ajax_update_sql', 'update_sql');        // 'update_sql' matches the 'action' in params

Is this the best solution? I don't know, but it works.

I've found a solution using Ajax with native Javascript as follows:

// Filename send2server.js
const sendToServer = function() {
   /* Prepare the object to be sent: ********************************************************************/
   var params = new FormData();
   params.append('action',   'update_sql');                // update_sql is implemented in PHP (see below)
   params.append('quoteAtt', props.attributes.quoteAtt);   // The actual data

   /* Create the Ajax connection object: ****************************************************************/
   var request = new XMLHttpRequest();
   request.open('POST', ajax_object.ajax_url, true);       // ajax_object.ajax_url defined in PHP (below)
   request.send(params);                                   // Send request to server
}

On the server side, the following functions receive the request in the following manner:

// File plugin.php
function load_ajax_script() {
    wp_enqueue_script(
        'send2server',
        plugins_url( 'send2server.js', __FILE__ ),
        array(),
        filemtime( plugin_dir_path( __FILE__ ) . 'send2server.js' )
    );

    wp_localize_script(                                // make ajaxurl available to Javascript
        'send2server', 
        'ajax_object', 
        array( 'ajax_url' => admin_url( 'admin-ajax.php' ) ) 
    );  
}
add_action('init', 'load_ajax_script');


function update_sql() {                                // Invoked by request.send()
    $received = $_POST["quoteAtt"];                    // Contents of quoteAtt
    // ...
}
add_action('wp_ajax_update_sql', 'update_sql');        // 'update_sql' matches the 'action' in params

Is this the best solution? I don't know, but it works.