Or rather, homelabs and home labs?
(image from Wikimedia)
Linear actuator, that’s literally how the commercial units work. Most are step capable either addon or built in and some have built in close resistance tests so you don’t mush the puppy or a kid or whatever is running about your house.
If you just Amazon automatic sliding door linear you’ll get results for units you can wire into your own setup. They’re Chinese but you can use it as a base to build better or simply an example to do the same.