Steps to Reproduce

1. Write ConversationHandler with conversation_timeout

Expected behaviour

The time of the last message should be stored in persistence, because after restarting, the job disappears.

Actual behaviour

After restarting the bot, the conversation does not end.

Operating System

Linux

Version of Python, python-telegram-bot & dependencies

python-telegram-bot 20.0
Bot API 6.4
Python 3.10.9 (main, Dec 19 2022, 17:35:49) [GCC 12.2.0]

Relevant log output

No response

Additional Context

No response