Equiv of `ssh a -tt ssh b` or how to use remote ControlMaster

Question

I have two servers, A and B. Login to B requires 2FA every time, so I use a ControlMaster to persist the authentication status.

However, I'm using a laptop, which sometimes sleeps and stops all TCP connections. This breaks the ControlMaster Socket. So I'm using another server as a jump server. I persist the authentication status on A and connect to B from A (ssh a -tt ssh b). I then write a RemoteCommand ssh -tt -q b to the ssh config for host a on my laptop, so I can just run ssh a.

However, the current setup doesn't work for VSCode's Remote SSH and rsync. How can I make this work?

Solutions I've tried:

1. ProxyJump. It don't work because I want to presist the authentication statsu on the jump server. I don't want to only use it as a network gateway.
2. Forwarding the 'control master socket` on A to my local laptop, then use it as socket to B. For some reason the ssh session on A isn't responding, so the ssh client on my laptop freezes.

Answer 1

I suggest creating a tunnel between A and B. Here's a rough a idea that you can test, then feel free to build upon it if it works:

On server a, run the following command

$ ssh -L 444:b:444

(444 is the port, you can replace it by any number you want)

This command will connect you to b and create a tunnel between a and b. Let this terminal run in the background.

Now back on your local computer, you just need to run

ssh a -p 444

And it will take you straight to server b