[v25.1.x] admin: handle service restart on shard 0

[vbotbuildovich]

Backport of PR #29519

[vbotbuildovich]

Retry command for Build#80103

please wait until all jobs are finished before running the slash command

/ci-repeat 1
skip-redpanda-build
skip-units
skip-rebase
tests/rptest/tests/random_node_operations_test.py::RandomNodeOperationsTest.test_node_operations@{"cloud_storage_type":1,"enable_failures":true,"mixed_versions":false,"with_chunked_compaction":false,"with_iceberg":true,"with_tiered_storage":true}

[vbotbuildovich]

CI test results

test results on build#80103

test_class	test_method	test_arguments	test_kind	job_url	test_status	passed	reason	test_history
PartitionBalancerTest	test_transfer_controller_leadership	null	integration	https://buildkite.com/redpanda/redpanda/builds/80103#019c29a6-46c9-48f3-a079-748531d681cf	FLAKY	8/11	Test PASSES after retries.No significant increase in flaky rate(baseline=0.4375, p0=0.9722, reject_threshold=0.0100. adj_baseline=0.8220, p1=0.0000, trust_threshold=0.5000)	https://redpanda.metabaseapp.com/dashboard/87-tests?tab=142-dt-individual-test-history&test_class=PartitionBalancerTest&test_method=test_transfer_controller_leadership
RandomNodeOperationsTest	test_node_operations	{"cloud_storage_type": 1, "enable_failures": true, "mixed_versions": false, "with_chunked_compaction": false, "with_iceberg": true, "with_tiered_storage": true}	integration	https://buildkite.com/redpanda/redpanda/builds/80103#019c29a6-46c3-4c92-be4a-07f976d7827d	FLAKY	9/11	Test FAILS after retries.Significant increase in flaky rate(baseline=0.0000, p0=0.0000, reject_threshold=0.0100)	https://redpanda.metabaseapp.com/dashboard/87-tests?tab=142-dt-individual-test-history&test_class=RandomNodeOperationsTest&test_method=test_node_operations

[pgellert]

/ci-repeat 1
skip-redpanda-build
skip-units
skip-rebase
tests/rptest/tests/random_node_operations_test.py::RandomNodeOperationsTest.test_node_operations@{"cloud_storage_type":1,"enable_failures":true,"mixed_versions":false,"with_chunked_compaction":false,"with_iceberg":true,"with_tiered_storage":true}