For other customers who might have the same question, here's some additional information uncovered by @elisadui and Celigo support:
In the Jira Cloud platform - NetSuite template, the flow Jira Cloud platform issues to NetSuite cases has a working example where the ticket status is updated in the opposite direction. See the mapping for issue.fields.status.name => Status (InternalId). Unfortunately, the bidirectional flow doesn't update the Jira status, as requested.
I am having a similar issue with a Salesforce -> Jira integration. Since status is updated via the "transitions" action, I cannot figure out how Celigo does (or can) map this transition.