Effectively, it’s referenced two times in the movie: once, when they can’t find the beacon thingy on Exegol (“How do you know it’s on that ship?” “A feeling.”); and once more, when Rey dies, so that Finn can “sense” it and react to it (“Rey…”).
Funny thing about this… apparently he just recognized the fact that it was the only non-Imperial Star Destroyer. He recognized it was made by the First Order. Apparently Pryde is on board Kylo’s Star Destroyer (the same one the gang raids earlier) that he brought to Exegol. This is the canon answer, in the novelization. I believe you can even tell the visual differences in the film. So Finn definitely didn’t need the Force to identify it, for what it’s worth.
EDIT: The reason why I think they needed to do this, plot-wise, was to both explain why Pryde was able to guide the ships out and also explain why they couldn’t just switch the signal to another Final Order Star Destroyer once his ship exploded. Apparently Palpatine instructed Pryde to modify Kylo’s destroyer with this special capability behind Kylo’s back. The other Final Order Star Destroyers don’t have this special signal carrier tech. Then again, this still doesn’t explain why the Final Order couldn’t just switch back to the radio tower when Pryde’s ship blew up. I think the Resistance probably should have blown it up as well to clear up that plot hole.