Yes, your understanding is correct!
You’re welcome to reuse your own previously made assets — including sprites, backgrounds, music, code, etc. — as long as you own the rights to use them. The important part is that the game/project you submit should be a new work created specifically for this jam.
As for an existing universe: yes, you can also create a completely new story set within a universe you’ve already established in another project. The existing worldbuilding/lore can carry over, as long as the actual game/story you submit is a new work made for this jam.
So you do not need to create a brand-new universe from scratch. Reusing your own creative assets and established worldbuilding is allowed; the new jam entry itself should be the new part.
Hope that clears things up, and thanks for asking beforehand!