My manager is all supportive of my promo from L4 to L5, but I am worried that my skip might be leaving the company. I can tell my skip is in a difficult position with their boss (director), so if my skip leaves the company, my confidence of getting promo will go down (my direct manager will stay for a while, though). So what kind of considerations should I have? Should I jump ship, just because of the fact that my skip might be leaving? Thank you
If your skip is supportive of your L5 case, then it will definitely hurt, but I don't think it'll hurt you that much.
While L4 -> L5 needs clearance up to director-level, that promotion is local enough where the immediate manager makes most of your case. Since your manager is supportive of your promotion (which is awesome), I recommend going through the promotion cycle and seeing what happens. Promotion chances are generally every 6 months, so you won't need to wait too long unless you literally just went through a cycle and missed it.
Best of luck! If you haven't already, I recommend going through this: [Course] Grow From Mid-Level To Senior Engineer: L4 To L5
Your manager is the most important person in your career.
Your skip is also important, but I certainly wouldn't make a career change simply because your skip might be leaving. Focus much more on your manager's advocacy for you, and how much political/social capital they have in the org. Ethan Evans talks about building the manager relationship in his course: Managing Up: Build Effective Relationships With Your Boss