How do I get the Messenger icon back on my iPhone 14 if it’s missing?

Put your finger on the middle of the screen and drag down to open Spotlight Search, and enter “messenger"

Or go to the last page of the Home screen, which is the app library, and find it there, then drag it to where you want it.

Are you asking about Apple Messages or FaceBok MEssenger? The similarity of names had caused a lot of confusion, so we need to clarify.