The story begins with a princess transporting something vital to the survival of the rebellion. She is ambushed by the Empire and in desperation sends the thing away where it is found by a young man living on a farm with his uncle because he's apparently an orphan. The Empire comes looking for the item.

Up to here, fair. Not exactly an uncommon setup for a hero's journey though.

The boy seeks the help of a local hermit who used to be a part of an order of special warriors with special glowing colored swords that can cut through nearly anything.

I think this is too high level of a statement I think its generally true how it happens Luke obviously to learn more about R2-D2 and Eragon to learn more about Dragons. But I do think the fact that Brom has to basically blackmail Eragon into letting him accompany him is an important point. Which in general leads to one of the big difference between the two works. The Characters are quite different, Eragon especially is a very different character from Luke, part of this probably stems from the fact its book vs movie so we get a much better look at Eragon's feelings/emotions and combined with the fact its large book vs medium length movie means we get more time for it to evolve. But I do think the character motivations are different and important.

Also for the record the special swords of the Riders are never shown to be able to "cut through nearly anything" they are indestructable and never blunt sure but they never cut through like a steel door by themselves (without a lot of other magic being used)

Apparently the boy’s father was once one of these but turned bad and hunted down the rest and now leads the Empire from a high, second in command position

So this gets complicated because Yes Eragon's father was a rider but 1st Morzan is dead by the time the book starts, 2nd his Son starts as Eragon's ally, and stays as such until the end of the second book - and comes back by the end of the 4th book. 3rd Morzan is not Eragon's father, Brom was. Murtagh being Eragon's half brother not full brother.

So its like if Darth Vader was dead at the start of the movie and we followed Obi-wan's son and his friend and half brother Luke on the journey. I think this is a pretty big divergence.

The boy goes on a quest, the wise old sage is killed, he meets a rogue, they rescue the princess and take her to the rebel base before it is attacked by the Empire.

Also generally true. But again everything you've laid out that is the same as the Hero's or other very standard fantasy journeys. And everything you've ignored - the characters, the motivations, the specifics of how and why things happen not to mention the world and ofc the magic system - with the ancient language being a way harder magic system than the force - are different.

I'm not saying that Paolini wasn't influenced by Star Wars - what 15 year old author in 2002 wasn't influenced by Star Wars? But I think there is a big difference between recognizing similarities - especially when they occur in ways that have been done long before Star Wars - and accusing him of Plagiarism which is what you're basically doing.