I have noticed the lag. I will update a Note from my MacBook Pro and when I go into my iPhone, it takes ten minutes for the changes to show up. In previous versions, I could be typing on my MacBook Pro and it would show up immediately on my iPhone. I think that this is more of an iCloud capacity issue than bugs so far. A lot of people are downloading iOS 13 and a lot of new customers are setting up new iPhones and iPads and I think that some iCloud services will just be slow for a while.