Hey @ryan38, thank you for reaching out!
I have a workaround that often pushes through updates stuck in a loop:
Go to file that defines this style. Then apply a small change to a property of the style. For example, like change the hex code or add a description - just something small that’s easy for you to remember and undo afterwards.
Publish the update
Go to a different file, accept library updates and see if you still get prompted to publish the same update.
Go back to the style and reverse whatever test change was applied.