Does this part matter?

Hi Josh,

It's a fairly safe bet those two pins are grounding contacts between the screen and the frame. Given that there are two of them and they're electrically connected to the same ground point, my personal opinion is that you will almost certainly be fine with just one.

That being said, if you do want to cover your a$$ and go ahead and fix the problem, what you'll need to do is replace the earpiece speaker, Here's the part showing those contacts.

Unfortunately iFixit doesn't have a guide to that repair, but the Nadie Me Llama Gallina website has just what you need. It's written in Spanish, but if you use it with the Chrome browser's translation feature, it is quite usable and well written.

Manuals / Apple iPhone 13 / Earphone - Nobody Calls Me Chicken

You can support iFixit's repair efforts by purchasing the part right here at iFixit's Store.

iPhone 13 Earpiece Speaker

As you work, take lots of pictures and once you're done you can use them to create your own iFixit guide to that repair. It's easy, fun, and the iFixit community will appreciate your efforts.

Update

Did the screen work before you broke that pin? Because truth be told, there's just no way missing either or both of those pins could cause the screen to fail. You can see from this picture that the two contact points go to the same piece of metal on the screen, so missing one of them wouldn't eliminate any signal from passing between the two points.

I'd suggest disconnecting the screen and checking both sides of the connector; you're looking for bent broken or missing pins. Use a magnifying glass and bright light and make sure the connectors are in good shape. If they are, check the length of the flex cable for any sharp bends or creases, or any physical damage such as a tear.

If everything's okay so far, clean both sides with 90% or higher concentration isopropyl (rubbing) alcohol, give it a hot minute to dry then carefully reconnect and retest.

If it still doesn't work, there's a strong possibility you may have gotten a bum screen; it happens even to iFixit. About the only way to verify that would be to try another screen, but if the old one is at least partially functional you could try plugging it in and seeing if it's still working the way it did previously. If it does, that's pretty good confirmation your replacement is a dud and you should pursue a warranty replacement.

So I'd say do some of this troubleshooting then come on back and let us know what you find.