She's trying to get the rest of the galaxy into the Galactic Union. That's not necessarily a bad thing, either, especially since she's trying to pull it off through diplomacy instead of military conquest. The Renza Federation is the next big chunk she'd really like to get to join. It appears to be comparable in size to Jurai or the Kuramitsu territory, maybe within an factor of two.
For the moment, relations with them are acceptable but they're still quite suspicious. So Seto permits Renza spies to work in her inner circle. She knows what they are, but they don't know that she knows. And she plays honest with them, too; they get to see her work, and they're always with her.
They learn that she's extremely devious, of course. But they also learn that her word is good. Sure, she manipulates people — but not, ultimately, to their detriment. If you think about it, all the people she plays around with end up benefiting from it. The spies will see that. Deep down, she isn't evil. People fear her because she's devious, and because she's extremely influential. In other words, she's the real power behind the throne, and letting Renza spies watch her operate helps them build confidence in her as a diplomatic partner.
The very end of the series is part of Seto's plan. With the Da Ruma guild shattered, the GP and Jurai don't need Seina's services anything like as much. Having the GP loan him and the Kamidake to the Renza Federation, and having Jurai loan Kiriko and the Mizuki, is a genuine gesture of good will because there's every reason to believe that they'll be just as effective at wiping out the Renza Federation's pirate problem as they were in GP territory. The merged ship is at a strength level of a first generation Royal Tree, and the pirates aren't going to have anything that can stand up to it.
Once he's completed his work in the Renza Federation, they're going to be genuinely grateful, and that will make it far, far easier for Seto to eventually convince them to join the Galactic Union.
Piracy is a scourge everywhere in the galaxy. Like as not this will happen again, with the next stellar empire that Seto wants to make friends with.
Which means Seina is going to go down in Galactic history eventually as the man who made it possible to unify the entire galaxy. As a diplomatic tool of Seto, of course, but nonetheless as the essential piece of that process. He is the ultimate goodwill ambassador representing Jurai and the GP, and thus the Galactic Federation. He is the pirate exterminator, the man who can wipe out more pirates in a week than an entire normal fleet can in ten years.
Seto looks to have been working on this project possibly for hundreds of years. Suddenly Seina makes it possible to complete it in just decades. It's no wonder Seto looks out for him so carefully, even to the point of begging Washu to give him the Kamidake. It would be interesting to know why Washu did it. One possibility is that Seto leveled with her. A different possibility is that Washu did it because Seina is Tenchi's friend.
It would also be interesting to know how early it was that Seto realized that Seina might be useful in this way. As crafty as she is, I think it occurred to her immediately, in the third episode, that he had that potential. Of course, Seina had a few surprises in store even for her, but I think that this may have been something she had in mind from a very early point, and that's part of why she sicced her girls, the Renza spies, on Seina and let them find out all about his gift.
Seto dangles that bait in front of them, and of course eventually they go for it. And then Seto magnanimously forgives them for the kidnapping, and uses her formidable influence to arrange the loan of the ship and the man as a goodwill gesture. It'll work, too. She's really the political operator, she is.
Seina is going to live a long time. And we've seen what happens when he isn't out hunting pirates; his bad luck kicks in full and he has a hard time. I think the answer is that he's going to spend his entire career hunting pirates. For the next several decades he'll be goodwill ambassador, the GP's pirate exterminator who gets loaned to other areas as a way of opening up positive diplomatic activities. Word will get around after he does his miracle in the Renza Federation, and other such groups will start to talk to Seto in hopes of eventually borrowing him.
Once the entire Galaxy is united, he'll serve as what amounts to a firefighter. Anywhere that piracy starts to flare up to unacceptable levels, he'll show up and bring it back under control. Piracy isn't going to go away, so he'll have work to do pretty much for the rest of his life.