It was supposed to be Leia’s doing. That’s why she dies doing it. She did a force thing similar to Luke’s death causing move in TLJ, with a hologram of someone.

It took Leia all the effort she apparently had to get the “spirit” of Han over to Ben. With that in mind, it would make sense that it took a little bit of time for him to get there. It’s unclear exactly how long it took Luke to get his hologram over to Crait.

By the time the lightsaber fight is over, the Falcon arrives to pick up Finn and Jannah off the wreckage. So, with it now up and running, it could have taken the Falcon any amount of time to get from (now Endor) to the Resistance base via hyperspace. The gap of time isn’t that bad here. It’s not hours on end. It could have been like a half an hour or less.

Leia has the medal. She probably brings it with her everywhere, especially after Han’s death about a year before EP 9. If we are to argue semantics and locations and timeframes, well then keep in mind that the dice are on the Falcon. Which Leia was not on or around when she decided to make her final move. So there you go, lol.

And yeah, they went with the medal so Chewbacca could get it. Because of the silly joke, sure, but it also still holds a meaning for these characters in-universe. Han, Luke, Chewbacca and Leia’s lives all changed after they met, and the medal symbolises that turning point for them. Han’s dice mean something to him alone, while the medal(s) mean something to the whole group. That feels kinda phony and silly to say, but it kinda works? Ehh?

These edits are just making all of this a little bit clearer.