Prompt input text lost when panel closes and reopens #54
Description
Bug Description
When you close the Symposium panel, whatever you've typed so far in the prompt input gets lost and is not restored when you reopen the panel.
Expected Behavior
The current prompt input text should be persisted and restored when the panel is reopened, similar to how other parts of the UI state are already persisted.
Current Behavior
Closing the panel discards any text typed in the prompt input field. Reopening the panel shows an empty prompt.
Notes
Other UI state is already being persisted - this is just a missing piece for the prompt input specifically.