sys.last_* not set for SyntaxErrors with IDLE

GitHub fields:

assignee = 'https://github.com/terryjreedy'
closed_at = None
created_at = <Date 2021-10-21.21:31:52.599>
labels = ['expert-IDLE', 'type-bug', '3.11']
title = 'sys.last_* not set for SyntaxErrors with IDLE'
updated_at = <Date 2022-01-27.05:46:40.336>
user = 'https://github.com/aroberge'

bugs.python.org fields:

activity = <Date 2022-01-27.05:46:40.336>
actor = 'terry.reedy'
assignee = 'terry.reedy'
closed = False
closed_date = None
closer = None
components = ['IDLE']
creation = <Date 2021-10-21.21:31:52.599>
creator = 'aroberge'
dependencies = []
files = []
hgrepos = []
issue_num = 45560
keywords = []
message_count = 6.0
messages = ['404669', '404711', '404712', '404713', '404716', '411840']
nosy_count = 2.0
nosy_names = ['terry.reedy', 'aroberge']
pr_nums = []
priority = 'normal'
resolution = None
stage = 'test needed'
status = 'open'
superseder = None
type = 'behavior'
url = 'https://bugs.python.org/issue45560'
versions = ['Python 3.11']