Short version: this book is really fun and well-written. If you are at all interested in the adventures of sixteen-year-old Leia, read it!
A few minor spoilers, but I've mostly tried to avoid them.
The book's spine is Leia's coming of age, in a very literal, ceremonial sense. Alderaani royal children aren't automatically heirs to the throne; they have to demand their position and prove themselves worthy first. This seems like a very Alderaan thing to do, and also works great for the story. The book starts with her "Day of Demand," when she formally demands to be invested as heir and publicly announces the challenges she'll undergo. In Leia's case, these are serving on the Apprentice Legislature, climbing a famous Alderaani mountain, and those "mercy missions" Vader is later so sarcastic about. They're genuinely hard challenges, too--we later learn that Breha had just barely attained the summit of that mountain when she had a nearly-fatal accident. Before attempting the climb, Leia prepares by taking a "pathfinding" class, in which she and other students are endangered or injured several times.
These challenges also put her in the way of all sorts of other emotional growth and plot stuff. She's already hurt that her parents seem to be growing apart from her, always "busy" and suddenly throwing a bunch of "dinner parties" for friends like Mon Mothma (I don't think it's really a spoiler to say they're getting serious about the Rebellion and want to protect Leia, because obviously). So she sees the challenges as a way to maybe get their attention again and prove she's an adult they can trust with their secrets. Of course, uncovering those secrets leads to trouble! Not uncovering them leads to even more trouble, however. In the Apprentice Legislature and pathfinding class, she also gets to spend time around a bunch of other teenagers for the first time, and realizes how little personal life she has. Maybe it's okay to do something for no reason other than it's fun sometimes? If only the Empire would stop ruining everything!
I really liked how it struck a balance between Leia being extremely competent and knowledgeable and also a teenager who is even younger and less experienced than in A New Hope. She and the rest of the Apprentice Legislature do a good job on an assignment, only to realize they'd been manipulated. She's really interested in the discussions she has with one of the guys in the Apprentice Legislature and pathfinding class about how Alderaan can best support freedom and a decent standard of living in the galaxy and stand up to the Empire without endangering the entire population...and he's also really cute. One of the other teenagers is such a weird girl...but hm, maybe there's more to her than Leia thought...wait, she's actually a good friend and super-useful for exciting anti-Imperial missions! And Leia evades suspicion on several occasions by taking advantage of the fact that all these adult Imperial men don't take teenage girls seriously. "Hm, maybe I should...cry? Yep, good plan!"
And her parents' desperation to protect her by keeping her out of the loop is both understandable and also really useful for causing plot trouble. She can't avoid accidentally wrecking some of the Rebellion's plans or endangering their bases if she doesn't know about them!
It's also really impressive how well the book handles references to other tie-in works. There's a bunch of them--but they work perfectly well within the context of this book alone, and I don't think you'd feel like you were missing an in-joke or waiting for the other shoe to drop if you didn't catch them. The arc of Leia getting to know that weird girl and becoming friends is a great story in itself, even if you haven't seen The Last Jedi and don't know Amilyn Holdo from a hole in the wall. The emerging rebel leaders arguing about how much violence is acceptable and whether that one guy is hurting the cause by being too extreme makes perfect sense even if you haven't seen Rogue One and don't know the name Saw Guerrera. And so on. Take notes, all other writers working in vast multi-media franchises!
(You probably do need to have seen the prequel trilogy to fully appreciate Leia's mercy mission to the miners of Onoam, however. What could go wrong on a moon of the Emperor's home planet Naboo, right? Well, maybe Leia's clothes will get dirty in the mine and she will have to borrow a dress from the Queen, and maybe they will feel compelled to make a courtesy call on the Emperor's good friend Panaka, and what if he thinks she looks familiar Leia has no idea the danger she's in oh no!)
Also, some bits are just really fun. Like the time Tarkin crashes one of those Rebel "dinner parties" and everyone's going oh shit what do we do.
All the threads of Leia forging relationships with other teenagers, figuring out her relationship with her parents, making political connections on her mercy missions, getting involved with the Rebellion, and earning her future right to the throne come together beautifully. And we get to see so much of Alderaan and Bail and Breha. That scene in A New Hope is going to be so much sadder now.
It is also a short, self-contained book, so you can have all the fun without committing to a seven-doorstopper arc with associated animated shorts and who knows what else. Recommended!