I don’t have the option for live wallpapers

Okay, I've been looking around on the internet.

Live Wallpapers are NOT supported on iPhone SE 2.Gen. But according to Apple's own support pages, it works with all iPhones except iPhone SE 1.Gen, elsewhere it says that Live Wallpapers do not work with iPhone XR, iPhone SE 1st and 2nd Generation.

my Friend with the exact same phone as me has the option to live wallpapers on wallpapers

If it's an iPhone SE 1st Generation then it does not support Live Wallpapers.

I do not usually use Live Wallpapers myself, but just tried to set up a Live Photo - and you are right. I am also not allowed to use Live Photo as Wallpaper. Can set an image, but it does not move.

It must be a software bug.