How to use paramiko to SSH

I have built below simple python code to connect to one of my webserver.

import paramiko

# Set up SSH client
ssh = paramiko.SSHClient()
ssh.set_missing_host_key_policy(paramiko.AutoAddPolicy())

# Set up connection details
ip = "10.218.16.16"
user = "user1"
password = "234!!!lem600@HW"

# Connect to server
try:
    ssh.connect(ip, username=user, password=password)
    print(f"Successfully logged in as {ssh.exec_command('whoami')[1].read().decode().strip()}")

except paramiko.ssh_exception.AuthenticationException:
    print("Authentication failed")
    
except paramiko.ssh_exception.SSHException:
    print("Unable to establish SSH connection")
    
finally:
    ssh.close()

This works fine. After connecting to this webserver, I am performing below steps in putty.

ssh user2@hadoopc1h1
Entering the password -235!!!lem600@HW

so what I need is to do the above also in same code... I have added below part also..

ip2 = "hadoopc1h1"
user2 = "user2"
password2 = "235!!!lem600@HW"


try:
    # Execute ssh command to connect to second server
    _, stdout, _ = ssh1.exec_command(f'ssh {user2}@{ip2}')

   
    stdin = stdout.channel.makefile("wb")
    stdin.write(f"{password2}\n".encode())
    stdin.flush()

    # Print output of ssh command to second server
    print(stdout.read().decode())

Here what I am getting

OSError: Socket is closed

Network connectivity is also available...can someone help me?

Solution

Tying to automate an interactive shell is usually wrong approach and will cause you troubles. Your attempt with exec_command is definitely a better start. See also
Providing input/subcommands to command executed over SSH with JSch

Though you might be actually looking for
How to SSH to a server behind another SSH server using JSch?