Not working for me on Android 16, additional taps of the "Check for update" button in the bottom-right don't change the fact that it says "Your system is up to date" and that the last change was last month.

I see same behavior on my 8.

Could be model-specific. I got the update by doing that manually on my Pixel 8 Pro, that also happens to be on the beta track so there are a few confounders. But that is the way to get the latest software that is waiting to be released to your phone, without waiting.