In SSHHook the timeout argument of the constructor is used to set a connection timeout. This is fine.

But in SSHOperator the timeout argument of the constructor is used for *both* the timeout of the SSHHook *and* the timeout of the command itself (see paramiko's ssh client exec_command use of the timeout parameter). This ambiguous use of the same parameter is very dirty.

I see two ways to clean the behaviour: 

1. Let the SSHHook constructor be the only way to handle the connection timeout (thus, if one wants a specific timeout they should explicitely build a hook to be passed to the operator using the operator's constructor).
2. Split the timeout argument in SSHOperator into two arguments conn_timeout and cmd_timeout for example.

The choice between 1 and 2 depends on how frequently people are supposed to want to change the connection timeout. If it is something very frequent. then go for 2. if not go for 1.

BR and thanks for the code!
airflow/providers/ssh/hooks/ssh.py
self.host_key = key_constructor(data=decoded_host_key)
                    self.no_host_key_check = False
        if self.pkey and self.key_file:
            raise AirflowException(
                "Params key_file and private_key both provided.  Must provide no more than one."
            )
        if not self.remote_host:
            raise AirflowException("Missing required param: remote_host")
        
        if not self.username:
            self.log.debug(
                "username to ssh to host: %s is not specified for connection id"
                " %s. Using system's default provided by getpass.getuser()",
                self.remote_host,
                self.ssh_conn_id,
            )
            self.username = getuser()
        user_ssh_config_filename = os.path.expanduser('~/.ssh/config')
        if os.path.isfile(user_ssh_config_filename):
            ssh_conf = paramiko.SSHConfig()
            with open(user_ssh_config_filename) as config_fd:
                ssh_conf.parse(config_fd)
            host_info = ssh_conf.lookup(self.remote_host)
            if host_info and host_info.get('proxycommand'):
                self.host_proxy = paramiko.ProxyCommand(host_info.get('proxycommand'))
            if not (self.password or self.key_file):
                if host_info and host_info.get('identityfile'):
                    self.key_file = host_info.get('identityfile')[0]
        self.port = self.port or SSH_PORT
    def get_conn(self) -> paramiko.SSHClient: