It was decided to start deprecating the asyncore, asynchat and smtpd modules in Python 3.6 released in 2016, 5 years ago. Python 3.10 emits DeprecationWarning.
Wait, only Python 3.10? According to the policy, the warning should be there for *at least* two releases. (That's a minimum, for removing entire modules it might make sense to give people even more time.)
The PEP 387 says "Similarly a feature cannot be removed without notice between any two consecutive releases."
It is the case here. The 3 modules are marked as deprecated for 4 releases in the documentation: Python 3.6, 3.7, 3.9 and 3.10. Example: https://docs.python.org/3.6/library/asyncore.html