I'm not sure if there's a limit for how long you can postpone a system update, but I think it can be at least days to even a few weeks. I manage my parents' Pixel 3a XL, and when I recently dropped by in the middle of September, I saw that the September update hadn't been installed yet (it was probably about 2 weeks after the update was released). I don't recall seeing any nag notifications, but then again, they don't do a great job of clearing their notifications.
That being said, I would say that system updates on Pixels have a much better track record in terms of lack of bugginess compared with other manufacturers because there's no tweaking that needs to be done for the update to match the various hardware and firmware for those other manufacturers' phones.