diff --git a/src/v/cloud_storage/partition_manifest.cc b/src/v/cloud_storage/partition_manifest.cc
index fb048579f0f3..68a5b9d4c945 100644
--- a/src/v/cloud_storage/partition_manifest.cc
+++ b/src/v/cloud_storage/partition_manifest.cc
@@ -744,7 +744,7 @@ void partition_manifest::set_archive_clean_offset(
 
 bool partition_manifest::advance_start_kafka_offset(
   kafka::offset new_start_offset) {
-    if (_start_kafka_offset_override >= new_start_offset) {
+    if (_start_kafka_offset_override > new_start_offset) {
         return false;
     }
     _start_kafka_offset_override = new_start_offset;
diff --git a/src/v/cloud_storage/tests/partition_manifest_test.cc b/src/v/cloud_storage/tests/partition_manifest_test.cc
index 1308fc901fd2..5cd2851c534b 100644
--- a/src/v/cloud_storage/tests/partition_manifest_test.cc
+++ b/src/v/cloud_storage/tests/partition_manifest_test.cc
@@ -1431,9 +1431,9 @@ SEASTAR_THREAD_TEST_CASE(test_partition_manifest_start_kafka_offset_advance) {
       m.get_start_kafka_offset_override(), kafka::offset(370));
     BOOST_REQUIRE_EQUAL(m.get_start_offset(), model::offset(100));
     BOOST_REQUIRE_EQUAL(m.get_start_kafka_offset(), kafka::offset(90));
-
+    // Allow update with the same value
+    BOOST_REQUIRE(m.advance_start_kafka_offset(kafka::offset(370)));
     // If trying to move back, it should no-op.
-    BOOST_REQUIRE(!m.advance_start_kafka_offset(kafka::offset(370)));
     BOOST_REQUIRE(!m.advance_start_kafka_offset(kafka::offset(369)));
     BOOST_REQUIRE_EQUAL(
       m.get_start_kafka_offset_override(), kafka::offset(370));
diff --git a/src/v/raft/state_machine_manager.cc b/src/v/raft/state_machine_manager.cc
index f8e6ddd1f31b..3fbe9bb3b0a3 100644
--- a/src/v/raft/state_machine_manager.cc
+++ b/src/v/raft/state_machine_manager.cc
@@ -215,7 +215,10 @@ ss::future<> state_machine_manager::apply_raft_snapshot() {
     co_await snapshot->reader.close();
     if (fut.failed()) {
         const auto e = fut.get_exception();
-        vlog(_log.error, "error applying raft snapshot - {}", e);
+        // do not log known shutdown exceptions as errors
+        if (!ssx::is_shutdown_exception(e)) {
+            vlog(_log.error, "error applying raft snapshot - {}", e);
+        }
         std::rethrow_exception(e);
     }
 }
diff --git a/tests/rptest/tests/random_node_operations_test.py b/tests/rptest/tests/random_node_operations_test.py
index a6b3f7de9cd6..a81cf2948ce6 100644
--- a/tests/rptest/tests/random_node_operations_test.py
+++ b/tests/rptest/tests/random_node_operations_test.py
@@ -29,9 +29,11 @@
 from rptest.clients.offline_log_viewer import OfflineLogViewer
 
 TS_LOG_ALLOW_LIST = [
-    re.compile("archival_stm.*Replication wait for archival STM timed out"),
+    re.compile(
+        ".*archival_metadata_stm.*Replication wait for archival STM timed out"
+    ),
     # topic deletion may happen before data were uploaded
-    re.compile("cloud_storage.*Failed to fetch manifest during finalize().*")
+    re.compile(".*cloud_storage.*Failed to fetch manifest during finalize().*")
 ]