add a class to account avatar in admin bar

Copy the whole wp_admin_bar_my_account_item() function to your functions.php:

rename the function to my_admin_bar_my_account_item.
and add the admin_bar_menu action to it:

add_action( 'admin_bar_menu', 'my_admin_bar_my_account_item', 10 );

/**
 * Add the "My Account" item.
 *
 * @since 3.3.0
 */
function my_admin_bar_my_account_item( $wp_admin_bar ) {
	$user_id      = get_current_user_id();
	$current_user = wp_get_current_user();
	$profile_url  = get_edit_profile_url( $user_id );

	if ( ! $user_id )
		return;

	$avatar = get_avatar( $user_id, 16 );
	$howdy  = sprintf( __('Howdy, %1$s'), $current_user->display_name );
	$class  = empty( $avatar ) ? '' : 'with-avatar myclass';

	$wp_admin_bar->add_menu( array(
		'id'        => 'my-account',
		'parent'    => 'top-secondary',
		'title'     => $howdy . $avatar,
		'href'      => $profile_url,
		'meta'      => array(
			'class'     => $class,
			'title'     => __('My Account'),
		),
	) );
}

And add your class (myclass) to this line as in the example:

$class  = empty( $avatar ) ? '' : 'with-avatar myclass';

https://codex.www.ads-software.com/Function_Reference/add_node

btw:
consider creating a child theme instead of editing your theme directly – if you upgrade the theme all your modifications will be lost.