In my experience on Odoo v16 only:

1. I can confirm that the 'Closed tasks' you want to set on a given task is only related to the column setting called 'Folded in Kanban' rather than anything else. By moving tasks into these specific columns you are then 'setting' a task closed.
   
   
2. It does not matter:
3. 1. What name the column has. For ex. you could have 2 columns in your Kanban board called 'Done' and 'Cancelled'.
   2. Where this column is positioned in your Kanban stage flow. Does not need to be at the right side.
      
      
4. More important is that each column can function to set tasks as Closed, as long as you configure the 'Folded in Kanban' parameter as TRUE:
5. 1. Click on the gear icon on the top of the column to access these settings:  

By setting this parameter you'll get something like this on your project task view (Kanban):

Now when I move the 'test' task to this column it will be considered Closed. To prove this, you can filter on 'Closed tasks' where that task should still be counted in the Done column:

When switching back to a filtered view with only open tasks, you should now see this this task no longer being considered 'Open'

Make sure you deactivate the 'closed tasks' filter

Additionally when the column Done is becoming to long, you can Archive items from that column by unfolding the Done column and then click the gear icon and choose 'Archive All':



I hope this helps you understand how Odoo behaves.