[PR #8717/e0a7c0cb backport][3.10] Minor tweaks backported from #8701 (#8719)

**This is a backport of PR #8717 as merged into 3.11
(e0a7c0c).**

Co-authored-by: Sam Bull <[email protected]>

Author: patchback[bot]

aiohttp/helpers.py

@@ -629,7 +629,7 @@ def register(
     def close(self) -> None:
         self._callbacks.clear()
 
-    def start(self) -> Optional[asyncio.Handle]:
+    def start(self) -> Optional[asyncio.TimerHandle]:
         timeout = self._timeout
         if timeout is not None and timeout > 0:
             when = self._loop.time() + timeout

aiohttp/multipart.py

@@ -2,6 +2,7 @@
 import binascii
 import json
 import re
+import sys
 import uuid
 import warnings
 import zlib
@@ -10,7 +11,6 @@
 from typing import (
     TYPE_CHECKING,
     Any,
-    AsyncIterator,
     Deque,
     Dict,
     Iterator,
@@ -48,6 +48,13 @@
 )
 from .streams import StreamReader
 
+if sys.version_info >= (3, 11):
+    from typing import Self
+else:
+    from typing import TypeVar
+
+    Self = TypeVar("Self", bound="BodyPartReader")
+
 __all__ = (
     "MultipartReader",
     "MultipartWriter",
@@ -280,8 +287,8 @@ def __init__(
         self._content_eof = 0
         self._cache: Dict[str, Any] = {}
 
-    def __aiter__(self) -> AsyncIterator["BodyPartReader"]:
-        return self  # type: ignore[return-value]
+    def __aiter__(self: Self) -> Self:
+        return self
 
     async def __anext__(self) -> bytes:
         part = await self.next()
@@ -581,7 +588,7 @@ class MultipartReader:
     response_wrapper_cls = MultipartResponseWrapper
     #: Multipart reader class, used to handle multipart/* body parts.
     #: None points to type(self)
-    multipart_reader_cls = None
+    multipart_reader_cls: Optional[Type["MultipartReader"]] = None
     #: Body part reader class for non multipart/* content types.
     part_reader_cls = BodyPartReader
 
@@ -602,10 +609,8 @@ def __init__(self, headers: Mapping[str, str], content: StreamReader) -> None:
         self._at_bof = True
         self._unread: List[bytes] = []
 
-    def __aiter__(
-        self,
-    ) -> AsyncIterator["BodyPartReader"]:
-        return self  # type: ignore[return-value]
+    def __aiter__(self: Self) -> Self:
+        return self
 
     async def __anext__(
         self,