Okay, I got it. @NigelG, you were right.
I had set a state on a group within the reusable element and it turns out that I need the state to be on the parent (not just a group within the element).
@NigelG thanks for your help!
Also, thanks @Kfawcett’s for your answer on another related question (and the example that I could play around with) Here’s that answer for anyone else coming across this thread: [SOLVED] Reusable element able to interact with elements on different pages?