I have 2 house rabbits (mini rex and dwarf hotot - both little high energy types from shelters). They have a “condo” that they sleep in when I’m at work, but otherwise they have the run of the place. I forgot to close the door of their house while I was at work once and they mostly just had a ball pulling all the clothes out of my laundry bin. There’s a nibble in a couple of my tshirts and a couple on chair legs, but they learned quickly what they are and are not allowed to chew. Cords are all inaccessible or protected in my home, but the rest is a matter of training and providing enough stimulation. Litter box training was easier than cats.
“Vegan kittens” are excellent pets for the right home. They essentially little long eared ponies as far as how their GI tracts and instincts work, so they’re not a good fit with little ones who might move too suddenly, handle rough, or sneak them rich treats. Like cats they can entertain themselves in a household with working people. But they’re social animals so unlike cats they don’t thrive without conspecific company - pairs tend to be healthier and happier than solo bunnies. And spayed/neutered bunnies are similarly both healthier and easier to manage than intact rabbits.
Mine prefer to stretch out next to me rather than sitting on my lap. One of mine sleeps in the end of my bed, hates socks and will try to tug them off your feet, and begs to be let out on my (bunny-safe) deck all the time. The other will melt right into the couch for extended petting and loves jumping obstacles so much that she got her own tiny set of jump standards and poles. They’re characters, to be sure!
Mine stay with a family member a few weeks per year while I’m abroad. Her old grumpy cat gives them a wide berth but otherwise ignores their existence and her younger, stronger prey drive cat is totally afraid of them. I’ve found all introductions to other species to be remarkably peaceful.
Rabbits are surrendered to shelters frequently but don’t have anywhere near the adoption rates of dogs and cats. Add to that the number of irresponsible breeders (and rates of reproduction in accidental breeding) and it becomes a no-brainer to adopt instead of shop. There are house rabbit society chapters and rabbit specific shelters all over the US.
I ended up with bunnies because I’m allergic to most house pets, but in case it’s not obvious from the text above, I think they’re pretty swell in their own right.