The management of Plans, for example create, delete, copy should be carried out using Planner Online (tasks.office.com).
The recommended method to copy a Plan is to open Planner in the Online version (tasks.office.com). Copy the required plan (please note the copy process requires a new name) and then add the new copy to Teams as a tab.
The renaming of a Plan should only be carried out via the Online version of Planner – tasks.office.com
Plans can be edited, and tasks added or removed using Microsoft Teams or Planner Online.
Plans can be deleted using Planner Online or MS Teams. Please note when deleting from Teams selecting the tick box during the delete process will not only remove the Plan but also remove the Plan from the backend SharePoint storage.
It is recommended not selecting the tick box and once you have checked the plan is not needed, removing it from SharePoint using the Planner Online version (tasks.office.com).
There is no Recycle Bin in Planner and only Microsoft can recover deleted files for a limited period of time.