'Why is my chatroom based on python sockets only allow one client to join?

When I have a client join the server, all is well. However, when I add another client and they try to send more than one message, the error

"Reading Error: "

shows up. Also, messages from clients don't show up on each other's screens. See the code below.

SERVER.PY

import socket
import select
HEADER_LENGTH = 10
global ipad
hostn = socket.gethostname()
ipad = socket.gethostbyname(hostn)
lol = "0.0.0.0"
IP = (lol)
PORT = 1234
# Create a socket
# socket.AF_INET - address family, IPv4, some otehr possible are AF_INET6, AF_BLUETOOTH, AF_UNIX
# socket.SOCK_STREAM - TCP, conection-based, socket.SOCK_DGRAM - UDP, connectionless, datagrams, socket.SOCK_RAW - raw IP packets
server_socket = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
# SO_ - socket option
# SOL_ - socket option level
# Sets REUSEADDR (as a socket option) to 1 on socket
server_socket.setsockopt(socket.SOL_SOCKET, socket.SO_REUSEADDR, 1)
# Bind, so server informs operating system that it's going to use given IP and port
# For a server using 0.0.0.0 means to listen on all available interfaces, useful to connect locally to 127.0.0.1 and remotely to LAN interface IP
server_socket.bind((IP, PORT))
# This makes server listen to new connections
server_socket.listen()
# List of sockets for select.select()
sockets_list = [server_socket]
# List of connected clients - socket as a key, user header and name as data
clients = {}
print(f'Listening for connections on {IP}:{PORT}...')
# Handles message receiving
def receive_message(client_socket):
    try:
        # Receive our "header" containing message length, it's size is defined and constant
        message_header = client_socket.recv(HEADER_LENGTH)
        # If we received no data, client gracefully closed a connection, for example using socket.close() or socket.shutdown(socket.SHUT_RDWR)
        if not len(message_header):
            return False
        # Convert header to int value
        message_length = int(message_header.decode('utf-8').strip())
        # Return an object of message header and message data
        return {'header': message_header, 'data': client_socket.recv(message_length)}
    except:
        # If we are here, client closed connection violently, for example by pressing ctrl+c on his script
        # or just lost his connection
        # socket.close() also invokes socket.shutdown(socket.SHUT_RDWR) what sends information about closing the socket (shutdown read/write)
        # and that's also a cause when we receive an empty message
        return False
while True:
    # Calls Unix select() system call or Windows select() WinSock call with three parameters:
    #   - rlist - sockets to be monitored for incoming data
    #   - wlist - sockets for data to be send to (checks if for example buffers are not full and socket is ready to send some data)
    #   - xlist - sockets to be monitored for exceptions (we want to monitor all sockets for errors, so we can use rlist)
    # Returns lists:
    #   - reading - sockets we received some data on (that way we don't have to check sockets manually)
    #   - writing - sockets ready for data to be send thru them
    #   - errors  - sockets with some exceptions
    # This is a blocking call, code execution will "wait" here and "get" notified in case any action should be taken
    read_sockets, _, exception_sockets = select.select(sockets_list, [], sockets_list)


    # Iterate over notified sockets
    for notified_socket in read_sockets:

        # If notified socket is a server socket - new connection, accept it
        if notified_socket == server_socket:

            # Accept new connection
            # That gives us new socket - client socket, connected to this given client only, it's unique for that client
            # The other returned object is ip/port set
            client_socket, client_address = server_socket.accept()

            # Client should send his name right away, receive it
            user = receive_message(client_socket)

            # If False - client disconnected before he sent his name
            if user is False:
                continue

            # Add accepted socket to select.select() list
            sockets_list.append(client_socket)

            # Also save username and username header
            clients[client_socket] = user

            print('Accepted new connection from {}:{}, username: {}'.format(*client_address, user['data'].decode('utf-8')))

        # Else existing socket is sending a message
        else:

            # Receive message
            message = receive_message(notified_socket)

            # If False, client disconnected, cleanup
            if message is False:
                print('Closed connection from: {}'.format(clients[notified_socket]['data'].decode('utf-8')))

                # Remove from list for socket.socket()
                sockets_list.remove(notified_socket)

                # Remove from our list of users
                del clients[notified_socket]

                continue

            # Get user by notified socket, so we will know who sent the message
            user = clients[notified_socket]

            print(f'Received message from {user["data"].decode("utf-8")}: {message["data"].decode("utf-8")}')

            # Iterate over connected clients and broadcast message
            for client_socket in clients:

                # But don't sent it to sender
                if client_socket != notified_socket:

                    # Send user and message (both with their headers)
                    # We are reusing here message header sent by sender, and saved username header send by user when he connected
                    client_socket.send(user['header'] + user['data'] + message['header'] + message['data'])

    # It's not really necessary to have this, but will handle some socket exceptions just in case
    for notified_socket in exception_sockets:

        # Remove from list for socket.socket()
        sockets_list.remove(notified_socket)

        # Remove from our list of users
        del clients[notified_socket] 

I think that the issue is in my server code, but I'll give you guys the client code for extra detail.

CLIENT.PY

import socket
import select
import errno
from cryptography.fernet import Fernet
import sys
key = Fernet.generate_key()
f_obj = Fernet(key)
HEADER_LENGTH = 10

global ipad
hostn = socket.gethostname()
ipad = socket.gethostbyname(hostn)

IP = (ipad)
PORT = 1234
my_username = input("Username: ")

# Create a socket
# socket.AF_INET - address family, IPv4, some otehr possible are AF_INET6, AF_BLUETOOTH, AF_UNIX
# socket.SOCK_STREAM - TCP, conection-based, socket.SOCK_DGRAM - UDP, connectionless, datagrams, socket.SOCK_RAW - raw IP packets
client_socket = socket.socket(socket.AF_INET, socket.SOCK_STREAM)

# Connect to a given ip and port
client_socket.connect((IP, PORT))

# Set connection to non-blocking state, so .recv() call won't block, just return some exception we'll handle
client_socket.setblocking(False)

# Prepare username and header and send them
# We need to encode username to bytes, then count number of bytes and prepare header of fixed size, that we encode to bytes as well
username = my_username.encode('utf-8')
username_header = f"{len(username):<{HEADER_LENGTH}}".encode('utf-8')
client_socket.send(username_header + username)

while True:

    # Wait for user to input a message
    message = input(f'{my_username} > ')
    

    # If message is not empty - send it
    if message:

        # Encode message to bytes, prepare header and convert to bytes, like for username above, then send
        message = message.encode('utf-8')
        encrypted_msg = f_obj.encrypt(message)
        message_header = f"{len(encrypted_msg):<{HEADER_LENGTH}}".encode('utf-8')
        client_socket.send(message_header + encrypted_msg)

    try:
        # Now we want to loop over received messages (there might be more than one) and print them
        while True:

            # Receive our "header" containing username length, it's size is defined and constant
            username_header = client_socket.recv(HEADER_LENGTH)

            # If we received no data, server gracefully closed a connection, for example using socket.close() or socket.shutdown(socket.SHUT_RDWR)
            if not len(username_header):
                print('Connection closed by the server')
                sys.exit()

            # Convert header to int value
            username_length = int(username_header.decode('utf-8').strip())

            # Receive and decode username
            username = client_socket.recv(username_length).decode('utf-8')

            # Now do the same for message (as we received username, we received whole message, there's no need to check if it has any length)
            message_header = f"{len(encrypted_msg):<{HEADER_LENGTH}}".encode('utf-8')
            message_length = int(message_header.decode('utf-8').strip())
            encrypted_msg = client_socket.recv(message_header).decode('utf-8')
            message = f_obj.decrypt(encrypted_msg)

            # Print message
            print(f'{username} > {message}')

    except IOError as e:
        # This is normal on non blocking connections - when there are no incoming data error is going to be raised
        # Some operating systems will indicate that using AGAIN, and some using WOULDBLOCK error code
        # We are going to check for both - if one of them - that's expected, means no incoming data, continue as normal
        # If we got different error code - something happened
        if e.errno != errno.EAGAIN and e.errno != errno.EWOULDBLOCK:
            print('Reading error: {}'.format(str(e)))
            sys.exit()

        # We just did not receive anything
        continue

    except Exception as e:
        # Any other exception - something happened, exit
        print('Reading error: '.format(str(e)))
        sys.exit()


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