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)

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.

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.