Structure can display the same columns as the Issue Navigator when showing search results.
You can toggle Issue Navigator columns by clicking Columns button in the Search toolbar.
When Issue Navigator columns are turned on, Structure temporarily switches to a system view that displays the same columns as Issue Navigator would display for that query. To switch back to your usual view, switch off the Columns button or switch off Search panel.
A separate columns configuration may be defined for a Saved Filter. When you use a saved filter in your JQL query (filter = "filter-name"), Structure detects that and will display columns defined for that filter. (If Columns button is turned on, of course.)
If you have a Progress column in the Issue Navigator, then the Structure's Progress column will be shown instead. The same applies to aggregate columns like Σ Original Estimate. Please keep in mind that these Structure columns and their JIRA counterparts work by different rules, and may display different values.