How can I achieve these smooth zoom effects seen in this video?
They start at 0:40, theyre like really smooth zoom transitions
this looks like it's using some of the Red Giant Universe plugins, specifically chromatic aberration, to create the odd bulging lens effect and they're probably just adding a few scale keyframes to enhance that effect. the keyframes clearly have a pretty heavy ease and in most cases it's either easing into an increased bulge and scale up or easing out of a decreasing bulge and scale down. There isn't really that much of a transition on these shots either. it's more a matter of timing out the animation around the edit to make it feel "right"
the "smoothness" you're looking for is probably mostly due to keyframe easing. I typically use a tool like Flow to keep my eases consistent