Welcome to the Community, @Amanda Crawford .
Yes, an Epic is a normal work item with its own Assignee and Status fields, and the timeline lets you add assignee and status as inline editable columns, that applies to epic rows the same as task rows.
What's likely throwing you off is that a parent row also gets a progress bar underneath it, rolled up from the status of its child items, green/blue/grey for done/in progress/to do. That bar is separate from the epic's own status field, and with no child items under this epic yet there's nothing to roll up, so that area stays blank.
- Confirm the Epic itself actually has an assignee set, an empty field shows as blank for any work item type, not just epics.
- Check the Fields/columns control on the timeline to make sure Assignee and Status are toggled on for the view.
Once both are true you should see the same owner avatar and status you get on tasks.
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