HI,
Thank you for the question.

There does not exist a function in BuddyPress API to achieve this currently.

We can create own own like this

/**
 * Returns total activities count for the user
 *
 * @param int $user_id user id.
 * @param string $type activity type.
 *
 * @return int
 */
function buddydev_get_total_user_activities_count( $user_id, $type = '' ) {
	global $wpdb;

	$table = buddypress()->activity->table_name;

	$where_conditions = array();

	$where_conditions[] = $wpdb->prepare( 'user_id = %d', $user_id );
	if ( $type ) {
		$where_conditions[] = $wpdb->prepare( "type = %s", $type );
	}

	$whe_sql = join( ' AND ', $where_conditions );

	return absint( $wpdb->get_var( "SELECT count(DISTINCT id) FROM {$table} WHERE {$whe_sql}" ) );
}

and use it like

$updates_count = buddydev_get_total_user_activities_count( 1, 'activity_update' );
$all_count = buddydev_get_total_user_activities_count(1)

and so on.

Regards
Brajesh

You need to print that using echo.

Example:-

echo "Count:" . buddydev_get_total_user_activities_count( 1, 'activity_update' );

Where 1 is user id.

Thank you for confirming.

Regards
Brajesh