Sony has started the Android 10 rollout for its phones out of the 8 phones on the list, it's the latest flagships that get it first. Users of the Sony Xperia 1 and Xperia 5 are reporting that they have received the notification for the update.
The software has a build number 55.1.A.0.748 and it includes the November 1 security patch (previously the phones were running the October patch). Those aside, the jump to Android 10 brings with it Dark mode and the new gesture navigation, plus a better overview of which apps are tracking your location.
Sony Xperia 1 running Android 10 (build number 55.1.A.0.748)
Anyway, the update weighs in at 725MB and will be available for download globally. It's still a staged rollout, though, starting in the US and Europe, so it may take a few days until you get the OTA update notification.
Note that some users are reporting issues with call and data connectivity post update, so you may want to wait for a new build to be released (you can't roll back to Android 9). There also seems to be an issue with getting to the Recent apps screen if you're using a custom launcher.
The six other eligible Xperias will have to wait until early next year for the OS upgrade.