[v23.3.x] CI Failure (BadLogLines: unknown exception thrown: seastar::gate_closed_exception) in `SIPartitionMovementTest. test_cross_shard `

[nvartolomei]

https://buildkite.com/redpanda/redpanda/builds/44819#018d8457-a020-42e9-aecf-17f9003a19b9

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

test_id:    rptest.tests.partition_movement_test.SIPartitionMovementTest.test_cross_shard.num_to_upgrade=2.cloud_storage_type=CloudStorageType.S3
status:     FAIL
run time:   2 minutes 48.213 seconds

    <BadLogLines nodes=docker-rp-6(1) example="ERROR 2024-02-07 17:02:20,750 [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 "/root/tests/rptest/services/cluster.py", line 142, in wrapped
    redpanda.raise_on_bad_logs(
  File "/root/tests/rptest/services/redpanda.py", line 1342, in raise_on_bad_logs
    raise BadLogLines(bad_lines)
rptest.services.utils.BadLogLines: <BadLogLines nodes=docker-rp-6(1) example="ERROR 2024-02-07 17:02:20,750 [shard 0:fetc] kafka - fetch.cc:1171 - unknown exception thrown: seastar::gate_closed_exception (gate closed)">

JIRA Link: CORE-1764

[piyushredpanda]

Not seen in at 6 weeks, closing