Jira Cloud integration not showing all issue types

Hoping that someone here has experience with this because Asana Support does not.

Our company uses both Asana and Jira for separate things. On some Asana projects we sync to an existing Jira project to keep the tasks up-to-date in both places. However, on one specific Jira project I can only sync Epics, not stories or tasks or bugs. We have contacted both Asana and Jira technical support and they point at each other and say it’s a permission setting but neither can advise.

As best as I can tell, I personally am missing some permission set in Jira since I am able to create Epics but not Stories. But I can’t figure out what it is or where it is hiding! I have full Admin priveledges in Jira for this project so theoretically, I should be able to do anything but in Asana I see Task, Story, and Bug as grayed out and can only choose Epic.