Juli Clover (MacRumors):

Customers who have purchased the new 2020 iPhone SE have found a surprising missing feature - Haptic Touch does not work with notifications.

On the 2020 ‌iPhone‌ SE, long pressing on a notification in the Notification Center or on the Lock screen does not appear to bring up rich notification options to allow ‌iPhone‌ SE users to interact with incoming content.

Matthew Panzarino (tweet):

I have not been able to determine whether there is any technical reason why or not. But it is ‘working as intended’ currently. I’m probably not an iPhone SE customer due to iPhone 11 camera stuff, but this would stop me from buying one.

It’s not that Haptic Touch isn’t present on the iPhone SE—it is—it just doesn’t seem to be enabled for notifications in the Notification Center or the Lock Screen. Other than this being a software defect, I cannot fathom why Apple would disable Haptic Touch in these two areas of the system.