Energy has no time. A Joule is one Neutron at a height of one meter. Power however does have time.
So a Joule per second is a Watt. I do think it is easy to get Energy and Power mixed up. This is not helped when units like kWh are used for Energy you see the h for hour and think there is some time component.
As Grizzly has said, in terms of dimensions, I'm afraid that's all wrong. The dimensions of energy include time^-2, hence the dimensions of power include time^-3.
When it comes to
units, you can, of course, choose ones which 'hide' some or all of the dimensions, but that doesn't alter the fact that they are there. For example, if you express a speed as mph or km/h, the time dimension is there 'for all to see'. However, if you express it as knots, then you can no longer 'see' the time dimension in the unit, although it is obviously still there. Even 'Watt' does not 'display' any time dimensions, although even you acknowledge that they are there.
Conversely, of course, one could use a unit which makes it appear that a time dimension is present, even when it isn’t. Taking the above example, a “knot.hour” would actually be a measure of distance, and includes no dimensions of time - but the unit makes it look as if it does.
Kind Regards, John