How to collect `log.error`(slf4j) into the Elastic APM "Error" app?

As far as I remember, this usage of the logger doesn't treat e as a Throwable, but as a parameter, assuming that the first argument is a parametrized message (ignored in this case because there is only one parameter in the provided message). Therefore, the agent doesn't treat it as a Throwable either.
If you use log.error("ouch apple=apple", e), you should get an error reported for that.