My daughter asked me recently, How do you go up to someone that you don’t know and talk to them? Today, you’re not only interrupting a social dynamic, you’re also interrupting people’s interaction with their devices. I notice it in my own family, because she comes up to me and I’m on my phone and I feel annoyed sometimes, like, I’m in the middle of reading, can’t you see?

It's all in the "excuse me". I think it becomes easy to think of the two words as just a saying that begins conversation, but I like to look at the actual meaning. It's an apology, no different from walking up to someone with an "I"m sorry, but..." or "Pardon me, but..."

So lean into that with your tone and body language. Begin your interruption of someone with a genuine apology for bothering them. Okay, good, so you did something wrong, but immediately apologized for it, and if everything follows the normal rules of politeness, the receiver will automatically forgive you for your interruption because you gave an earnest apology for a very minor social infraction. You are now at a neutral position with the person, having done nothing particularly wrong or right, but you now have their attention and can say/ask whatever.

If you want to practice, try practicing with a compliment. "Excuse me ... pause for response, if positive/neutral then... that's a really nice hat you're wearing. Just thought I'd let you know." and end conversation. Nothing really gained or lost here, but you got to practice some, and very few people will care about the interaction enough to give you more than a second's thought afterward.