Fix resizing window closes and stops execution of Duo

What does this MR do and why?

When the browser window is resized from full screen to a smaller breakpoint, the Duo Chat panel is automatically hidden. This causes any running workflow to pause/stop, interrupting the user's task.

This MR decouples workflow execution from the panel's visibility state, ensuring workflows continue running in the background even when the chat panel is hidden due to window resizing.

Screenshots

fix_workflow_execution_bug_1080p.mov

References

Resizing window closes and stops execution of Duo (#581137)

How to set up and validate locally

1. Open Duo Chat and start a workflow.
2. Resize the browser window to a smaller breakpoint.
3. Verify that the workflow continues executing in the background.
4. The chat panel should hide but the workflow should not be interrupted.