Recently a few Google Pixel 6 and Pixel 7 owners have reported seeing the January 2023 Play system update available for download after being stuck on the November update for months. This issue of getting Google Play system updates almost three months late is becoming an issue that Pixel users are concerned about.
This was not the case for yours truly, as I was able to apply the update and after a reboot the Google Play system update showed a date of January 1, 2023. The update is around 63 megabytes in size when installed on the Pixel 7, and approximately 59 megabytes when installed on the Pixel 6 series.
To check which version of Play system update you have on your Pixel, go to Settings > About phone > Android version. In that section, you will see the versions for both the Android and Google Play system updates, which should ideally both match the same month. To check if you have an update available for Google Play, tap that section to check for an update. If you are still on an old version of Google Play services and no updates show as available when tapping on that section, make sure that your Google Play Store is up to date, although that does not guarantee an update.
Source: Phone Arena