[v24.3.x] stm/shutdown: moar logging

[vbotbuildovich]

Backport of PR #26311

[vbotbuildovich]

CI test results

test results on build#66729

test_class	test_method	test_arguments	test_kind	job_url	test_status	passed	reason
CloudRetentionTest	test_cloud_retention	{"cloud_storage_type": 2, "max_consume_rate_mb": 20}	ducktape	https://buildkite.com/redpanda/redpanda/builds/66729#01973454-405d-4fbe-9358-1dac7fb97407	FLAKY	3/21
CloudRetentionTest	test_cloud_retention	{"cloud_storage_type": 2, "max_consume_rate_mb": null}	ducktape	https://buildkite.com/redpanda/redpanda/builds/66729#01973454-405c-4a69-8285-2926b3230dee	FLAKY	20/21	upstream reliability is '18.69158878504673'. current run reliability is '95.23809523809523'. drift is -76.54651 and the allowed drift is set to 50. The test should PASS
CloudStorageTimingStressTest	test_cloud_storage_with_partition_moves	{"cleanup_policy": "compact,delete"}	ducktape	https://buildkite.com/redpanda/redpanda/builds/66729#01973454-405b-4fad-9b39-fef9b5d6da09	FLAKY	18/21	upstream reliability is '96.29629629629629'. current run reliability is '85.71428571428571'. drift is 10.58201 and the allowed drift is set to 50. The test should PASS
ShadowIndexingWhileBusyTest	test_create_or_delete_topics_while_busy	{"cloud_storage_type": 2, "short_retention": true}	ducktape	https://buildkite.com/redpanda/redpanda/builds/66729#01973454-405c-4a69-8285-2926b3230dee	FLAKY	15/19	upstream reliability is '28.39506172839506'. current run reliability is '78.94736842105263'. drift is -50.55231 and the allowed drift is set to 50. The test should PASS
RandomNodeOperationsTest	test_node_operations	{"cloud_storage_type": 2, "enable_failures": false, "mixed_versions": false, "with_iceberg": true, "with_tiered_storage": false}	ducktape	https://buildkite.com/redpanda/redpanda/builds/66729#01973454-405d-4fbe-9358-1dac7fb97407	FAIL	0/10
RandomNodeOperationsTest	test_node_operations	{"cloud_storage_type": 2, "enable_failures": false, "mixed_versions": false, "with_iceberg": true, "with_tiered_storage": true}	ducktape	https://buildkite.com/redpanda/redpanda/builds/66729#01973454-405d-4fbe-9358-1dac7fb97407	FLAKY	1/10
RandomNodeOperationsTest	test_node_operations	{"cloud_storage_type": 2, "enable_failures": true, "mixed_versions": false, "with_iceberg": true, "with_tiered_storage": false}	ducktape	https://buildkite.com/redpanda/redpanda/builds/66729#01973454-405d-4fbe-9358-1dac7fb97407	FAIL	0/9
RandomNodeOperationsTest	test_node_operations	{"cloud_storage_type": 2, "enable_failures": true, "mixed_versions": false, "with_iceberg": true, "with_tiered_storage": true}	ducktape	https://buildkite.com/redpanda/redpanda/builds/66729#01973454-405d-4fbe-9358-1dac7fb97407	FAIL	0/10

[bharathv]

logging only change, failures unrelated.