CI Failure (`exception thrown: seastar::gate_closed_exception`) in `SIPartitionMovementTest.test_cross_shard`

[vbotbuildovich]

https://buildkite.com/redpanda/vtools/builds/11761

Module: rptest.tests.partition_movement_test
Class: SIPartitionMovementTest
Method: test_cross_shard
Arguments: {
    "num_to_upgrade": 2,
    "cloud_storage_type": 1
}

test_id:    SIPartitionMovementTest.test_cross_shard
status:     FAIL
run time:   235.428 seconds

<BadLogLines nodes=ip-172-31-4-143(1) example="ERROR 2024-02-08 01:02:41,032 [shard 0:fetc] kafka - fetch.cc:1171 - unknown exception thrown: seastar::gate_closed_exception (gate closed)">
Traceback (most recent call last):
  File "/usr/local/lib/python3.10/dist-packages/ducktape/tests/runner_client.py", line 184, in _do_run
    data = self.run_test()
  File "/usr/local/lib/python3.10/dist-packages/ducktape/tests/runner_client.py", line 269, in run_test
    return self.test_context.function(self.test)
  File "/usr/local/lib/python3.10/dist-packages/ducktape/mark/_mark.py", line 481, in wrapper
    return functools.partial(f, *args, **kwargs)(*w_args, **w_kwargs)
  File "/home/ubuntu/redpanda/tests/rptest/services/cluster.py", line 168, in wrapped
    redpanda.raise_on_bad_logs(
  File "/home/ubuntu/redpanda/tests/rptest/services/redpanda.py", line 1413, in raise_on_bad_logs
    raise BadLogLines(bad_lines)
rptest.services.utils.BadLogLines: <BadLogLines nodes=ip-172-31-4-143(1) example="ERROR 2024-02-08 01:02:41,032 [shard 0:fetc] kafka - fetch.cc:1171 - unknown exception thrown: seastar::gate_closed_exception (gate closed)">

[michael-redpanda]

Similar failure to #16586. Could be same issue. Starting with enterprise team until source of gate closed exception found (since fetch caught it)

[dotnwat]

So, this can be considered a duplicate of https://github.com/redpanda-data/redpanda/issues/16532 and was resolved by https://github.com/redpanda-data/redpanda/pull/16554.