First of all, I don’t think “Luke sneaking into his apprentice’s room” is a huge deal to start with. It’s his nephew, it’s not that creepy. Not to mention it wasn’t his intent to kill Ben when he entered, I honestly doubt he even considered the possibility beforehand.

Second of all, it’s not like he hacked into his laptop and looked at Ben’s search history. Luke was searching Ben’s feelings, this is something Jedi do practically 24/7. He just decided to do it when Ben was asleep because that would give him the clearest picture. Is that a bit of a breach of privacy? Sure, of course it is (though not to the extent you’re making it out to be). Luke was afraid of Ben’s potential. He wanted to find out what was in his heart, and what his future was. Could he have handled the situation better? Yes, but that’s the point. In his hubris he thought he could take matters into his own hands. When he realized his mistake, it left him with shame and consequence.