[Cache Bug] The same workflow/prompts hit cache should still notify the front-end

I have a workflow, I generated an image once in a tab of the browser, and then I opened another tab without making any changes and triggered the same task, but the browser did not show any effect.

Reproduce the same workflow in two browser tabs without changing it, then trace how a cache hit is handled and how the front end is notified. Done means the second tab visibly responds when the cached task is triggered, but the issue does not name files or tests to start from.

Written by the indexing model from the issue text.