AFAIK Lambda and everything else will use micro-VMs. No serious company would use a shared kernel design for workloads in different security contexts. (Personally I wouldn't even use the same hardware host, but sometimes sacrifices have to be made)

Like others have said, this will get you root inside the container. It isn't a container escape. File/volume mounts shared across containers would be vulnerable.

Firecracker is extremely hardened, so I wouldn't worry about Lambda. As for ECS, getting root doesn't necessarily mean you have a container escape. I think you could escape containers with this exploit, but you would need a different payload than what's published. I could be wrong though.

I would assume AWS is pretty on the ball when it comes to handling stuff like this if they didn't have other defenses or mitigations in place already.