When a Power Card is played for less than its total cost (e.g., via "Unlock the Gates of Deepest Power"), does that reduce the cost to Repeat it via "Powerstorm" or other effects that Repeat a Power based on its cost?

When a Power Card is played for less than its total cost (e.g., via "Unlock the Gates of Deepest Power"), does that reduce the cost to Repeat it via "Powerstorm" or other effects that Repeat a Power based on its cost?

No, being able to play a Power Card for less than its printed cost does not reduce the cost printed on the card. Use that printed cost for anything else that references the cost of the Power Card.