diff --git a/distributed/shuffle/_shuffle.py b/distributed/shuffle/_shuffle.py
index 007992b4d2b..c42f6d94426 100644
--- a/distributed/shuffle/_shuffle.py
+++ b/distributed/shuffle/_shuffle.py
@@ -2,11 +2,12 @@
 
 import logging
 import os
+import pickle
 from collections import defaultdict
 from collections.abc import Callable, Collection, Iterable, Iterator, Sequence
 from concurrent.futures import ThreadPoolExecutor
 from dataclasses import dataclass
-from functools import partial, cached_property
+from functools import cached_property, partial
 from pathlib import Path
 from typing import TYPE_CHECKING, Any
 
@@ -21,7 +22,7 @@
 
 from distributed.core import PooledRPCCall
 from distributed.exceptions import Reschedule
-from distributed.protocol import dask_serialize, dask_deserialize
+from distributed.protocol import dask_deserialize, dask_serialize
 from distributed.shuffle._arrow import (
     check_dtype_support,
     check_minimal_arrow_version,
@@ -89,27 +90,27 @@ def __init__(
         self.partition_id = partition_id
 
     def load(self) -> LoadedPartition:
-        with handle_unpack_errors(self.partition_id):
+        with handle_unpack_errors(self.shuffle_run.id):
             try:
                 data = self.shuffle_run._read_from_disk((self.partition_id,))
             except KeyError:
                 data = None
-        return LoadedPartition(data, self.shuffle_run.meta, self.partition_id)
+        return LoadedPartition(data, self.shuffle_run.meta, self.shuffle_run.id)
 
 
 class LoadedPartition:
     def __init__(
         self,
-        data: list[pa.Table],
+        data: list[pa.Table] | None,
         meta: pd.DataFrame,
-        partition_id: int,
+        shuffle_id: ShuffleId,
     ):
         self.data = data
         self.meta = meta
-        self.partition_id = partition_id
+        self.shuffle_id = shuffle_id
 
     def convert(self) -> pd.DataFrame:
-        with handle_unpack_errors(self.partition_id):
+        with handle_unpack_errors(self.shuffle_id):
             if self.data is None:
                 data = self.meta.copy()
             else:
@@ -118,35 +119,36 @@ def convert(self) -> pd.DataFrame:
 
 
 @dask_serialize.register(UnloadedPartition)
-def _serialize_unloaded(obj: UnloadedPartition):
-    import pickle
-
-    # Convert to LoadedPartition when serialized. Note that
+def _serialize_unloaded(obj: UnloadedPartition) -> tuple[tuple[ShuffleId], list[bytes]]:
+    # Convert to LoadedPartition before serializing. Note that
     # we don't convert all the way to DataFrame, because this
     # adds unnecessary overhead and memory pressure for the
     # cudf backend (and minor overhead for pandas)
     loaded = obj.load()
-    return (loaded.partition_id,), [pickle.dumps(loaded.meta), pickle.dumps(loaded.data)]
+    return (loaded.shuffle_id,), [
+        pickle.dumps(loaded.meta),
+        pickle.dumps(loaded.data),
+    ]
 
 
 @dask_serialize.register(LoadedPartition)
-def _serialize_loaded(obj: LoadedPartition):
-    import pickle
-
-    return (obj.partition_id,), [pickle.dumps(obj.meta), pickle.dumps(obj.data)]
+def _serialize_loaded(obj: LoadedPartition) -> tuple[tuple[ShuffleId], list[bytes]]:
+    return (obj.shuffle_id,), [pickle.dumps(obj.meta), pickle.dumps(obj.data)]
 
 
 @dask_deserialize.register((UnloadedPartition, LoadedPartition))
-def _deserialize_loaded(header, frames):
-    import pickle
-
-    partition_id = header[0]
+def _deserialize_loaded(
+    header: tuple[ShuffleId], frames: list[bytes]
+) -> LoadedPartition:
+    shuffle_id = header[0]
     meta = pickle.loads(frames[0])
     data = pickle.loads(frames[1])
-    return LoadedPartition(data, meta, partition_id)
+    return LoadedPartition(data, meta, shuffle_id)
 
 
-def _get_partition_data(part, barrier_key):
+def _get_partition_data(
+    part: UnloadedPartition | LoadedPartition | pd.DataFrame, barrier_key: int
+) -> pd.DataFrame:
     # Used by rearrange_by_column_p2p to "unwrap"
     # UnloadedPartition/LoadedPartition data after
     # a P2PShuffleLayer
@@ -369,7 +371,7 @@ def cull(
             return self, culled_deps
 
     @cached_property
-    def _tokens(self):
+    def _tokens(self) -> tuple[str, str]:
         token = tokenize(self.name_input, self.column, self.npartitions, self.parts_out)
         _barrier_key = barrier_key(ShuffleId(token))
         return token, _barrier_key