really should use iPhone SE screen protector?

Apple has never stated that any recent iPhone uses Gorilla Glass, which is a trademark of Corning Glass Works. That doesn't mean that the glass is either stronger or weaker than Gorilla glass, just that it probably isn't Gorilla Glass, or they would say if it was. I've never used a screen protector on any iPhone in 10 years. And I've never scratched or broken one. You should never carry any smartphone loose in a pocket; use either a slip case or a belt holster. Cases with a flip over flap are not a good choice, as he flap can cover the noise cancellation mic on the back when it is flipped open.

As with many things in life, there is a tradeoff in glass between hardness (scratch resistance) and frangibility (fracture resistance). You can't have both, so most manufacturers choose a compromise in between. A screen protector will prevent scratches to the phone's screen by providing a scratchable (and replaceable) overlay, but it won't make it any less likely that the screen will break if you drop the phone. To reduce the chance of it breaking on a drop, a rubber bumper case will help.