I do wonder if the narrative nature might be tricky to DM, for me anyways, as I’m not particularly good at improv in the moment. Be curious to hear people’s experience of that.
I have several thoughts on this.
Firstly, as I mentioned previously, it doesn't have to fall to the GM alone; players are encouraged to pitch suggestions for the dice results, so don't be afraid to draw on them (it's not to the taste of every group, but it's an option). Secondly, as also mentioned, the book has preset examples of what the results can be used for, so feel free to use them - they're not as narratively satisfying, but they're a decent fallback, and can be dramatic in the right situation. eg. 3 threat to cause "out of ammo" isn't terribly exciting by itself, but if it occurs in the middle of a firefight where the group are pinned down in a cantina, surrounded by Stormtroopers? Well, now they have to get a bit more creative.
Next, remember that improv is a skill like any other and the only way to improve is practice, which means failing sometimes; but also, the best improvisers have a deep well to draw from, so immersing yourself in as much Star Wars media as possible should help deepen the well you draw from for the game (read: liberally copy from). Once I became familiar with FFGSW, I found it difficult to not see how certain scenes could be translated into mechanics. Let's take the rescue of Leia scene:
After clearing the control room of Imperials, Han tries to deal with the alarm by radioing in that the situation is under control and rolls a failure, causing the Imps to send a squad of Stormtroopers. Luke, Leia, Han and Chewy are subsequently pinned down in the cell banks as the Stormtroopers block the only way out. Leia borrows Luke's blaster to shoot open a vent (her player hoping it opens a duct to escape through); it's an easy check, but Leia doesn't have much in the way of a Ranged dice pool as she was built as a diplomat. The GM spends a dark side Destiny point to upgrade the difficulty from a single purple difficulty die, to a single red challenge die. Leia rolls success, but also Despair: the vent is open, and the characters now have a way out (the success), but it leads to a trash compactor and oh, no, it's operational (the Despair)!
So once you're familiar with both the mechanics and the media touchstones, it becomes easier to reverse engineer one to the other.
Lastly, a rule of thumb: success should give the players what they the aiming for, failure should deny them their goal, advantage should give them a benefit separate from their goal (though, ideally, related to it), and threat should cause a problem distinct from failure. For example, success with threat shouldn't deny the character what they achieved, but could introduce a new problem to resolve; meanwhile, failure with advantage might prevent the characters achieving their goal but provide an alternate route to it, or alleviate the current pressure to give them breathing room to come up with a change of plan.