_check_banner timeout for subsequent lines

Hello,

I am doing ssh over ssm, and while I can set the banner_timeout for the first line, the subsequent lines still fail unless I increase the timeout there. The error I get below has been discussed many times, but I am able to fix it only if I overwrite the timeout in the else clause of the _check_banner method here: https://github.com/paramiko/paramiko/blob/main/paramiko/transport.py#L2269

Why doesn't the else clause also respect the banner timeout?

Traceback (most recent call last):
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/paramiko/transport.py", line 2139, in _check_banner
    buf = self.packetizer.readline(timeout)
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/paramiko/packet.py", line 367, in readline
    buf += self._read_timeout(timeout)
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/paramiko/packet.py", line 577, in _read_timeout
    raise socket.timeout()
socket.timeout

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/paramiko/transport.py", line 1966, in run
    self._check_banner()
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/paramiko/transport.py", line 2144, in _check_banner
    "Error reading SSH protocol banner" + str(e)
paramiko.ssh_exception.SSHException: Error reading SSH protocol banner

Traceback (most recent call last):
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/paramiko/transport.py", line 2139, in _check_banner
    buf = self.packetizer.readline(timeout)
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/paramiko/packet.py", line 367, in readline
    buf += self._read_timeout(timeout)
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/paramiko/packet.py", line 577, in _read_timeout
    raise socket.timeout()
socket.timeout

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "/Library/Frameworks/Python.framework/Versions/3.6/bin/fab", line 10, in <module>
    sys.exit(program.run())
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/invoke/program.py", line 363, in run
    self.execute()
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/invoke/program.py", line 532, in execute
    executor.execute(*self.tasks)
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/invoke/executor.py", line 129, in execute
    result = call.task(*args, **call.kwargs)
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/invoke/tasks.py", line 128, in __call__
    result = self.body(*args, **kwargs)
  File "/Users/matt/work/leo-radar/deploy/fabfile.py", line 158, in test
    ctx.run('printenv | grep HOSTNAME')
  File "<decorator-gen-3>", line 2, in run
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/fabric/connection.py", line 29, in opens
    self.open()
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/fabric/connection.py", line 615, in open
    self.client.connect(**kwargs)
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/paramiko/client.py", line 397, in connect
    t.start_client(timeout=timeout)
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/paramiko/transport.py", line 587, in start_client
    raise e
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/paramiko/transport.py", line 1966, in run
    self._check_banner()
  File "/Library/Frameworks/Python.framework/Versions/3.6/lib/python3.6/site-packages/paramiko/transport.py", line 2144, in _check_banner
    "Error reading SSH protocol banner" + str(e)
paramiko.ssh_exception.SSHException: Error reading SSH protocol banner

Start in paramiko/transport.py at the _check_banner method and inspect how the timeout is passed for the first and subsequent banner lines, focusing on the else clause linked in the issue. Confirm the intended banner_timeout behavior for delayed subsequent lines and add coverage using the repository’s existing test structure. Done means subsequent lines no longer fail when they require the configured banner timeout.