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.
There have been complaints about the missing feature on Reddit and the MacRumors forums. From Reddit:
I received my SE yesterday and very quickly realized that Haptic Touch is not supported on notifications. I am not seeing this reported anywhere, haven’t seen one review mentioning it, no video I watched mentioned it. Haptic Touch works for peek and pop, and on icons on the home screen but if you are on the lock screen or Notification Center and try to long press an email to archive, or a text to quick reply you are out of luck.
On the 6S-XS 3D Touch was the solution, with the XR and 11 series Haptic Touch was the replacement, but this is the first non 3D Touch phone to be released where all the features of Haptic Touch are not fully baked into the OS
With Haptic Touch-enabled devices like the iPhone 11 and 11 Pro, long pressing on a notification in the Notification Center or the Lock screen brings up interactive options based on the app sending the notification. An Apple News notification, for example, brings up options for reading the full story, sharing a story, or saving for later, while an email app might offer options to reply and delete an incoming message without needing to open the app.
In our testing, we were not able to long press on a notification to view these interactive options, as the long press functionality did not work. We also tried on an iPhone 8, which the iPhone SE is based on, but we were able to get the rich notifications to work on that device, which has 3D Touch.
While iPhone SE users cannot long press on notifications on the Lock screen or in the Notification Center, there does appear to be a Haptic Touch option when pressing on an incoming notification when the iPhone is in use.
A Reddit user called Apple Support and was told there was no software update planned to fix the behavior, but Apple Support can be unreliable when it comes to information about new hardware releases.