A gif animation has very few frames, so you could do it in Photoshop as frame-by-frame animation. Cut out the plants from the background and clone the missing spots so that you have the room without the plants. Then duplicate the plant layer and use liquefy to move them some, duplicate again and move them some more. Animate so that the background and just one of the plant layers is visible at a time, one plant layer after another. Somewhere between 5 and 10 frames will be fine for a gif animation.
You could certainly do this in After Effects, but if you’re not familiar with the program, it’ll take significant time since you’ll have to study the basics first. It’s a very different animal from Photoshop.