Rejected by a company six months ago and they just reopened the same role. Reapply or leave it?

I got to the final round and lost to someone else, and they said they'd keep me in mind. Since then I've worked on exactly the thing their feedback mentioned.

Part of me says just apply, part of me worries it looks desperate or that my old interview notes are sitting in their system waiting. Has anyone gone back to a company after a no?