When you Preview a Rule’s Execution history, you can see many pieces of detail, except the ‘Rule Run Date’. You would have to refer to the email notification to check the rule run date. It would help when re-running for a different Rule Date to have the ability to see the Run Date either in the Blue bar or in the View Logs section of the Execution History in the UI.
Example of what you see in the email notification:

Example placeholder locations within the Preview/Execution History:
