Meta box does not save or update

The reason that the field is not saving is due to the nonce check in my_content_save() failing. Changing the nonce check to the following code will fix the issue:

if (!wp_verify_nonce( $_POST['content_overview_nonce'], 'content_overview_save' )){
    return;
}

The nonce check should use the content_overview_save action because that is what was specified here:

wp_nonce_field( 'content_overview_save', 'content_overview_nonce');

Note that there was also a missing > in the #page_content_overview_metabox input field. For the sake of completeness, here’s the full updated code:

class my_metaboxes{

    public function __construct() {
        add_action( 'add_meta_boxes', array( $this, 'my_overview_metabox' ) );
        add_action( 'save_post', array( $this, 'my_content_save' ) );
    }

    public function my_overview_metabox(){
        add_meta_box( 
            'page_overview_metabox', 
            'Page content overview', 
            array( $this,'content_overview_metabox' ), 
            'post', 
            'advanced', 
            'high' 
        );
    }

    public function content_overview_metabox( $post ) {
        wp_nonce_field( 'content_overview_save', 'content_overview_nonce' );
        $value = get_post_meta( $post->ID, '_post_content_key', true );

        echo '<input type="text" id="page_content_overview_metabox" name="page_content_overview_metabox" value="' . 
     esc_attr( $value ) . '" placeholder="Enter the page overview details" style="width: 100%; height:120px;">';

    }

    public function my_content_save( $post_id ){
       if ( ! isset($_POST['content_overview_nonce'])){
            return;
       }

       if ( ! wp_verify_nonce( $_POST['content_overview_nonce'], 'content_overview_save' ) ) {
            return;
       }

       if ( defined( 'DOING_AUTOSAVE' ) && DOING_AUTOSAVE ) {
            return;
       }

       if ( ! current_user_can( 'edit_post', $post_id ) ) {
            return;
       }

       if ( !isset( $_POST['page_content_overview_metabox'] ) ) {
            return;
       }

       $my_data = sanitize_text_field( $_POST['page_content_overview_metabox'] );
       update_post_meta( $post_id, '_post_content_key', $my_data );
       }
}

new my_metaboxes();