This is caused by the JiraIssueParameterValue's getValue() method having the same signature as its superclass method, but a different return type.
This means class.getMethods() returns two different entries, one for String and one for Object. The Exported annotation apparently applies to both these methods (probably because it only considers signatures?), so both get serialized independently.
This is looks like a bug in Stapler, which assumes getMethods() has no "duplicates", caused by a very unusual case in the Jira Plugin.
Possible workarounds for Jira plugin, that would fix this issue for past releases of Jenkins core/Stapler:
- Export a new method public String value() instead, so the Exported annotation does not apply to the supertype method
- Change the return type of getValue() to Object, so there won't be two entries in JiraIssueParameterValue.class.getMethods() for getValue. Minor changes to other methods in the same class need to be done (add a few toString() calls).
Since Stapler issues are tracked elsewhere, reassigning this to the Jira Plugin which could apply one of the workarounds mentioned above.