Not all users are getting the new Google Assistant at the same time. So if you don't have it yet (and you'll know if you do because it looks noticeably different) don't worry as it'll show up in due time. Maybe even before the end of the day. Or at least the weekend.
The new Google Assistant for G Suite users is a gradual rollout
Based on comments in the Reddit thread where users have reported this showing up, it seems to be a gradual rollout.
There are only about 29 comments on the post at the time of writing, and at least a couple of users have stated they don't have it on their Pixel 4 series device.
Google sends out updates for many of its services as staggered rollouts. Not all the time, but often enough. So that's likely what's happening here.
Sending out the updates in a slower fashion also allows Google more control over the flow of things to make sure the update is smooth.
Worth pointing out is that it's unclear if this is related to an update for the Google app or if Google is just turning it on for users server side. More than likely it's the latter.
You should receive a full-screen pop-up to download Assistant data
According to the poster an on-screen pop-up showed up on their phone that told them they were able to download Google Assistant data.
Clicking the download button resulted in them being treated with the new UI. Which comes with a sort of translucent gradient-like design that keeps the visuals underneath the overlay still visible. To a degree.
It also comes with continual conversations. Overall it has a new look and some new functionality. So it's no wonder that G Suite users have been eager to get their hands on it.
This should be rolling out for both the Pixel 4 and the Pixel 4 XL. So if you have either device keep an eye out for changes. It seems to be a waiting game, and it probably won't do any good to try and update the Google app.