Avid doesn’t do a paste attributes in the same way as FCP, but are are a few ways of doing a very similar thing.
A thing I do a lot is to drag the effects to a bin, rename tham so that I know what each one does, and drag them onto each media clip that I want the effect on.
If you want the same effect across a sequence, put the effect(s) on the video layer(s) above the cut shots, using add edit to set the start and end points for the effect on the track. [If you don’t already know, you can use clip effects for transition effects in this way.]
If a shot has several effects on it that you want to duplicate, sometimes it’s worth duplicating that shot (with it’s effects) into the place where you want to see the new shot, then step in and replace the old shot with the new one at the “bottom” level, below the effects as it were.