iPhone SE keeps shutting down

80% is generally considered by Apple to be the point a new battery should be installed, but constant restarts or freezes can be software or other hardware related.

To rule out software you would normally Restore the device, preferably as “New” via iTunes, that way you have a clean iOS and no thirdly party apps to muck things up. You can use the “Erase” option under Settings to achieve similar but you are left with the original OS so it’s not as thorough.

Restore your iPhone, iPad, or iPod to factory settings - Apple Support

If following the Restore it’s still happening then you need to make a Genius appointment to either get the battery looked at or the hardware tested.

The first area to check would be battery health, this may help and depending on what you discover will dictate what’s done next.

iPhone Battery and Performance - Apple Support