While there's no direct connection it usually is a positive step or sign and often enough is followed by decision made/PPR. (Heck, any movement is positive). Unfortunately not consistent between visa offices as to whether they send it or not.That was the same for me.... nothing for a couple of weeks and just got my pre-arrival letter for what that is worth I don't know. Plus, it seems there are plenty of PRs granted where a pre-arrival letter wasn't sent (or at least the spreadsheet wasn't updated which is more likely).
BUT: getting pre-arrival so soon (if your file is july 2021) is moving pretty quick.
I think the wildcard aspect for pre-arrival and timelines after it is security and criminality; for USA/NATO countries, these are often easier and quicker.