Using native SharePoint 2016. user can access the page.
After the user changes the navigation and then click 'OK' it shows the "AccessDenied.aspx".
When we go back to the site we can see the updates(navigation done).
So the user has the permission to update the navigation.
When I add the permission :
"Manage Web Site - Grants the ability to perform all administration tasks for the Web site as well as manage content."
The associated permission is:
Add and Customize Pages - Add, change, or delete HTML pages or Web Part Pages, and edit the Web site using a Microsoft SharePoint Foundation-compatible editor.
And then user can update navigation without the "AccessDenied.aspx" page.