As of now, native JIRA worklogs do not support custom fields. The only solution to this is using a different time tracking provider that overwrites JIRAs default behaviour.
Are there plans to offer this module Time Tracking Provider in Forge context?
Easier than that would probably be to allow the creation of custom fields for worklogs in general.
In my case, we would use this to store an external reference to enable a 3rd party syncronization.