No social skills needed, you just need to be honest. So say that you'll leave because the current work is boring/stressful and the will let you choose the project you want if you are any good. Also usually they want to put their best developers on the most interesting problems so they'd ask you to do it anyway.

There's a skill to being honest in a productive way. Being honest in a way that communicates your thoughts and gets people engaged rather than defensive is really difficult but really valuable. But if you don't yet have that skill being completely honest will hinder you.

Maybe we are just thinking of different things when we talk about social skills? I think of things like being able to participate in small talk all day or participating in social events. I am very good at reading people and understand how they think and how they would react to different things I say, so in some way I got good social skills, but I'm pretty sure most people would say that I have bad social skills since I don't like social situations and therefore don't build connections.

Honestly? That's not how development works at all, in my experience. Best developers aren't isolated on "most interesting problems", but rather, are getting constantly sucked into war rooms and emergency calls. And when they are working on "interesting problems", they are constantly working, verbally and in writing, to convince reluctant management and other engineers to agree to their new, "interesting" approach to the problem in question. Those are massively social behaviors. "Being honest" is necessary but not sufficient. Understanding people's motivations, finding reasons for them to believe your idea is beneficial for them and their own interests, that's what gets you what you want.

Here's an example. I am trying to do important, interesting work, but I'm often interrupted, because I work in DevOps and wind up drawn into other people's problems. So on the whiteboard next to my desk, I wrote my two "Wildly Important Goals" (from the book Four Disciplines of Execution), and underneath that, the sentence "If something does not apply to these goals, why am I doing it?" This became quite the controversy, but it works! It has significantly reduced my interruptions. That's social skill in action.