When I click on the "?" (question mark) associated with the Content Token Reference in the Editable Email Notification section of the Jenkins project configuration page, I see the following documentation of the ${LOG_REGEX} token:

${LOG_REGEX}
Uses a regular expression to find a single log entry and generates a new output using the capture groups from it. This is partially based on the description-setter plugin (https://github.com/jenkinsci/description-setter-plugin).

That's missing any explanation of how to specify the regex and the new output.

Without knowing how to specify those, the token is unusable.