From the perspective of narrative power scaling, Luke Skywalker would seem to easily beat the gem empire. RotJ Luke has a Narrative Defense (a character's ability to resist changes or narrative effects targeted at them, "plot armor", the ability to avoid or survive attacks, but also the ability to avoid being tricked, convinced away from their beliefs, waylayed, or otherwise be manipulated by other characters) that, like most other protagonists, is quite high [surviving the rancor, surviving jabba's troops, not being turned to the dark side, surviving the fight with vader, surviving attacks from the emperor, etc] but his Narrative Offense (a character's ability to force narrative effects or changes to occur, the ability to defeat and kill, but also the ability to trick, convince and outsmart, the ability to generally force scenes to "go in their direction" and to cause scenes to occur at all) is also very high for a protagonist [forcing his way into Jabba's palace, bypassing all his defenses, killing the rancor and Boba Fett, getting to Yoda, getting to Darth Vader, beating Vader in the fight, convincing him to return to the light, etc]
On the other hand, as best as I can tell, the gem empire's Narrative Offense is quite weak for a Villian. Basically everything they did successfully occurred off screen (which makes it inadmissable for narrative power scaling as it's just lore, and not an actual event in the narrative), their in-show successes (based on my reading of the wiki) seem to be limited to temporarily capturing a couple characters and killing a couple people. Their Narrative Defense is also extremely weak (which isn't exactly unexpected from a Villian), with them seemingly easily being outwitted by the protagonists at every turn, including being talked out of their evil-ness in a 45 minute episode.
From this, we can conclude that Luke Skywalker (as of RotJ) would easily defeat the Gem Empire. Given the length of the gems' defeat in its original series, it's likely that Luke could defeat them in a 30 minute special, or perhaps even a 22 minute standard tv episode.
(note: I haven't seen most of Steven Universe, so all of my analysis of the Gem Empire was based on its wiki article. If the Gems' did anything especially affecting on screen that I missed do feel free to inform me)
I like how you take into account the narrative functions. My main concern is that Luke’s lightsaber is probably made of the same stuff as white diamonds arm. So while the likelihood of him defeating them is high, I’m much more concerned about the how.
I feel like the obvious argument against that is that “touching the gems doesn’t hurt humans, so it won’t hurt Luke, right? “ but Luke is not human. He comes from a completely different galaxy and time, and happens to look like us. It’s pretty well established that lightsabers are pure light, and very painful to most species in his galaxy. You have to keep in mind that the gems are also said to be light projections, and are likely from a different place and age. Considering the circumstances, they are likely within our own galaxy.
Regardless, I’m curious to see how plot armor saves Luke from an army of living light sabers.