The Google Pixel 3 series received its timely security patch but along with it, Google bundled a fix that should take care of the emergency calling bug. Even though last October was the end of the road for the duo in terms of major software updates it's nice that the company still addressed this issue.
The build number is SP1A.210812.016.A2 and is available for download to most users, including Verizon-locked ones. The patch itself is just 500KB big. After applying you will be able to call 911 without issues.
As we mentioned earlier, Android 12 is the last major update for the Pixel 3 and 3 XL and this is likely the last update overall as Google made an announcement last November saying that users should expect the last patch coming in Q1 2022.