Python docker sdk: exec_run kills the ssh socket

Question

need some help here :).

I have 2 containers A and B running on my host machine. /tmp dir is configurated as a volume in A and is volume mounted to B. Container A starts B with:

docker run -d --init --it --privileged --name container_B --env SSH_AUTH_SOCK -v /tmp:/tmp --port 2222:22

So that B will run in detached mode and stay alive.

In container A, I need to attach to B and run some commands, here is my code, I'm using the python docker SDK:

import docker
import os
class RunCommands:
  def __init__(self, name): 
     self.SSH_AUTH_SOCK = os.environ["SSH_AUTH_SOCK"]
     self.docker_client = docker.from_env()
     self.container = None
     self.container_name = name
     ...

  def run_commands(self):
    # 1st time: ssh keys are loaded correctly
    res = subprocess.run(["ssh-add", "-L"], stderr=subprocess.STDOUT,
                        stdout=subprocess.PIPE, check=True, text=True)
    print(res.stdout)

    env_vars = {
      "SSH_AUTH_SOCK": self.SSH_AUTH_SOCK,
    }
    commands = [
                r"""
                bash -c "echo 'hello'"
                """
    ]
    self.container = self.docker_client.containers.get(
                self.container_name)
    # run some commands
    for command in commands:
      exec_result = self.container.exec_run(
        cmd=command, tty=True, stream=True, privileged=True, environment=env_vars)
      for line in exec_result.output:
        print(line.decode('utf-8', errors='ignore'), end='', flush=True)

    # 2nd time: Error!
    res = subprocess.run(["ssh-add", "-L"], stderr=subprocess.STDOUT,
                        stdout=subprocess.PIPE, check=True, text=True)
    print(res.stdout)

So the ssh agent is alive and keys are loaded (tested with the 1st time "ssh-add -L"), but after A attached to B and run exec_run() with SSH_AUTH_SOCK forward to B, ssh-add -L failed with:

Error connecting to agent: No such file or directory
subprocess.CalledProcessError: Command '['ssh-add', '-L']' returned non-zero exit status 2

Seems like B killed the ssh socket after the execution of the commands even though it's still alive (detached mode). Can anyone explain this to me? How can I prevent this from happening? I need the ssh agent to do other things in A. Thank you!