Coroutines & async generators disagree on the iteration protocol semantics

GitHub fields:

assignee = None
closed_at = None
created_at = <Date 2021-09-02.20:32:30.403>
labels = ['interpreter-core', 'type-bug', '3.10', '3.11']
title = 'Coroutines & async generators disagree on the iteration protocol semantics'
updated_at = <Date 2021-09-03.03:26:08.506>
user = 'https://github.com/1st1'

bugs.python.org fields:

activity = <Date 2021-09-03.03:26:08.506>
actor = 'yselivanov'
assignee = 'none'
closed = False
closed_date = None
closer = None
components = ['Interpreter Core']
creation = <Date 2021-09-02.20:32:30.403>
creator = 'yselivanov'
dependencies = []
files = []
hgrepos = []
issue_num = 45088
keywords = []
message_count = 1.0
messages = ['400951']
nosy_count = 4.0
nosy_names = ['gvanrossum', 'lukasz.langa', 'yselivanov', 'pablogsal']
pr_nums = []
priority = 'normal'
resolution = None
stage = 'needs patch'
status = 'open'
superseder = None
type = 'behavior'
url = 'https://bugs.python.org/issue45088'
versions = ['Python 3.10', 'Python 3.11']