Can't use structlog.stdlib.ProcessorFormatter with structlog_sentry.SentryProcessor

At first, guys, thanks for the very useful lib!

I've tried to achieve the same logging format for both logging and structlog packages. Next I've tried to configure sentry in compound with structlog and structlog_sentry. All is good, but I have one issue that bothers me a lot.

structlog.stdlib.ProcessorFormatter have try/except closure to detect was the record wrapped by structlog.stdlib.ProcessorFormatter.wrap_for_formatter or not.
https://github.com/hynek/structlog/blob/9aa02f2bdacf57b9ea943ff7f3e82d0840032bf4/src/structlog/stdlib.py#L502-L511

And structlog_sentry.SentryProcessor by design on each record tries to extract exc_info if record has suitable level.

In the case like

logging.getLogger("default_logging_logger").error("some simple error")

I will get

in Sentry, that is not correct.

The issue covers in structlog_sentry.SentryProcessor._get_event_and_hint in

structlog-sentry/structlog_sentry/__init__.py

Line 42 in c15fdb0

exc_info = event_dict.get("exc_info", True)

I'd like to propose to use in SentryProcessor exc_info = event_dict.get("exc_info", False) instead of True as default value of event_dict.get

Expected behaviour is to get just an error without bounded exc_info if exc_info=True didn't passed explicitly.

Here is gist of my code with structlog / logging configuration + logger.error() call:

https://gist.github.com/yoshi-lyosha/9766b6759b674297fcc698a331ba6ca6