So I found out it is in fact an animation bug, not really a cooldown bug. When you charge the healing pulse, phoenix holds the circle thing in his hand. I expect this circle thing to be there. If it is not there, I (mistakenly) assume that my input didn’t come through. So I release and repress mouse 1. (I switch to pulse with 4)
This obviously causes it to go on cooldown, as the game just sees a regular use of healing pulse.
The reason I let go early, is because sometimes phoenix does not perform the appropriate animation while charging healing pulse. If you hold mouse 1 really quickly after switching to weapon slot 4, the animation can be skipped. The healing is properly applied regardless. I thought it was a cooldown bug because I let go of mouse 1 early because I thought it wasn’t registering my input due to the absence of the animation. Maybe the animation could be fixed so that it will correctly play when used rapidly after switching to weapon slot 4.