`logging.log` doesn't naively work as audit hook for `sys.addaudithook`

Bug report

Documentation for sys.addaudithook states "Hooks can then log the event [...]".
This works when I don't log, but instead print:

sys.addaudithook(print)
id(0)  # printed

However, nothing gets logged when I follow the suggestion to log, like:

sys.addaudithook(functools.partial(logging.warning, 'Audit hook %s %s'))
id(0)  # NOT logged

The cause is that logging.Logger._log (called by logging.warning) tries to find the caller (to populate module, lineno, funcName log format fields). For this, logging.Logger._log itself then causes audit events, which again call the audit hook. That results in infinite recursion, i.e. a RecursionError exception, which aborts the audit hook, and silences logging.

Workaround

By (temporarily) modifying logging._srcfile, the attempt to find the caller is skipped (and the log format fields are instead populated as "unknown"), infinite recursion and exception are prevented, and logging does happen:

sys.addaudithook(functools.partial(logging.warning, 'Audit hook %s %s'))
logging._srcfile = None  # prevent finding caller
id(0)  # logged

This is existing functionality, only (?) documented in source (file logging.__init__, line 188: "Setting _srcfile to None will prevent findCaller() from being called. This way, you can avoid the overhead of fetching caller information"). Though it works, the workaround is hard to find and not ideal.

Solutions

• Ideally, logging should not attempt to gather caller info in an audit hook (however, this requires tight coupling of the logging and sys modules, so they understand each others' internals)
• Equally user-friendly, audit events would not be generated within audit hooks (that risks incompleteness of auditing, but so does silencing logging)
• Less user-friendly, a keyword parameter (e.g. find_caller: bool = True) could be added to the signature of each log function, logging.Logger._log can inspect it, and the documentation for sys.addaudithook should recommend to use find_caller=False for logging in audit hooks

# logging.Logger._log
if logging._srcfile and find_caller:
    ...

# to use
sys.addaudithook(functools.partial(logging.warning, 'Audit hook %s %s', find_caller=False))
id(0)  # logged

• At the minimum, the documentation for sys.addaudithook should recommend above workaround, i.e. temporarily set logging._srcfile = None

def my_log(event, args):
    save_srcfile = logging._srcfile
    logging._srcfile = None
    logging.warning('Audit hook %s %s', event, args)
    logging._srcfile = save_srcfile

sys.addaudithook(my_log)
id(0)  # logged

Environment

The above issue exists in all Python versions supporting sys.addaudithook, i.e. 3.8, 3.9, 3.10, and 3.11.
I tested on 3.8.10, 3.9.13, 3.10.4, and 3.110rc2 on Windows 11 64 bit.

Reproduce the recursion using the sys.addaudithook and logging.warning examples, then read logging.init, especially Logger._log, findCaller(), and the _srcfile note, alongside the sys.addaudithook documentation. Determine which proposed behavior or documentation change is acceptable and verify that audit-hook logging no longer recurses or silently fails.