You must enable Motion Sense to use gesture controls. 🙂
On Nest Hub (2nd gen), you can turn Motion Sense on or off to start or stop detecting movement. Note: Motion Sense needs to be on to perform Quick Gestures and Sleep Sensing.
Check out THIS link.
We have a mixture of 1st and 2nd gen Nest Hubs; I've never seen anything in the Google Home app that tells us that it's a 1st or 2nd gen device except for individual settings.
The screen capture you shared is for the 2nd gen Nest Hub; it shows "Quick Gestures" and is the same as what we see for our 2nd gen Nest Hub.
Gestures (https://support.google.com/googlenest/answer/9449279?hl=en&co=GENIE.Platform%3DiOS) are different from swiping (https://support.google.com/googlenest/answer/9137285?hl=en&co=GENIE.Platform%3DiOS#zippy=%2Cuse-your...) on the Nest Hub. I don't know why you can't swipe, though I have seen a few posts about it. You could try rebooting it in the Google Home app by selecting the Nest Hub, selecting Settings, then the "more" option (the 3 dots) in the upper right corner, and then "Reboot". Or you can unplug it for a minute and plug it back in.
Chiming in-- have you noticed any changes on its behavior? Can you provide us the cast firmware version of your Google Nest Hub?
To check which firmware version you're on, follow these steps:
Keep us posted.