I can tell you that if your kids are not too nosey you can achieve something close to it.

It has been a while since I set this up for my kid and we moved away a year or two ago since well, kid got nosey and I moved to selfhosting with Jellyfin, but this should still work.

There are options to remove autoplay, remove comments and show the bookmarked/playlist tab first. I think you can switch off all the other tabs too, so that pretty much the only tab you can see is playlists. And when a video plays there are no weird comments to see and it does not move to the next video.

Now you can make custom playlists of what you want your kid to access and it will look like folders of videos in the app. Just teach your kid how to navigate that and there you go, they can only watch those videos.

Up until they get too curious, the search bar could not be deactivated I think, so if they click there and type random letters they might stumble over random shit. Also, every video has the icon of the channel its from and when you tap it you do get to see all of their content. So you have to check if channels you take videos from are not containing anything adult level. But most cartoon channels don't so the worst that can happen is that they see cartoons you might not want them to see.