Answer
If the entire process requires a time T, then the power supplied is $\frac{mgh}{T}$.
The time that the lifting takes does matter. The path taken doesn’t affect the power, if and only if the two paths take the same time.
Work Step by Step
Power is the rate at which work is performed.
The work done on the suitcase depends on the height of the table and the weight of the suitcase.
If the table top is a height h above the floor and the suitcase has mass m and weight mg, the amount of work done is exactly mgh.
