Honestly why would you want baby gates to be a permanent fixture in your home?

This might be an easier/less expensive option if you don’t mind a gate.

https://www.littlevictorian.com/diy-dog-gate-for-cheap-3-75/

Below is a link with info around install of your idea and not an easy process it seems. https://alittlehouse.wixsite.com/littlehouse/post/pocket-pet-gate

I'm guessing dog owners. I've never seen this before, but it's a lot nicer of a look than having baby gates up in perpetuity for the dogs.

The chances of this being possible are slim - walls not thick enough, mechanicals and posts in the walls, etc. A carpenter is who you’d need to ask.