Log exception so traceback contains timestamp and level?

[Skip Montanaro]

The logging package can log exceptions and call stacks, but it does
(in my opinion) a suboptimal job of it. Consider this simple example:

>>> import logging
>>> FORMAT = '%(asctime)-15s %(levelname)s %(message)s'
>>> logging.basicConfig(format=FORMAT, force=True)
>>> log.warning("msg", stack_info=True)
2021-02-06 20:46:52,399 WARNING msg
Stack (most recent call last):
  File "<stdin>", line 1, in <module>

It formats the warning message just fine, but simply dumps the
traceback onto the stream with no timestamp or level. For my purposes,
this is more important for exceptions. (I'm just using the stack trace
feature as it's easier in a small example.) I would like to call
something like

log.exception("Some message...")

and find something like this in the output stream:

2021-02-06 20:46:52,399 ERROR Some message...
2021-02-06 20:46:52,400 ERROR Traceback (most recent call last):
2021-02-06 20:46:52,402 ERROR   File "<stdin>", line 1, in <module>

That way I can more easily grep log files for errors and get the
entire detail, including the traceback. It seems I have to subclass
logging.Formatter to override formatStack or formatException, then
construct the individual lines of output, set handler and formatter,
blah blah blah.

I'm pretty sure I've done this in the past by writing my own little
log_exception method which formats the exception and calls log.error
for each row of the traceback. That seems easier than the "right" way.
That seems harder than it ought to be. Hopefully I'm just missing
something simple.

Skip