Allow the inclusion of `exc_info` on a per handler basis.

This allows showing the `exc_info` if a specific log level or lower is
enabled, but, on a per logging handler basis.
For example, if the console hander is at info level and the file log
handler is on debug level and we pass `exc_info_on_loglevel` to a log
call, the traceback will be included in the log message of the file
handler but not on the log message of the console handler.

Closes #14870
Closes #14859