Looking at the execution plan, it is hard to see how deleting a row (at the Clustered Index Delete) then inserting it again (at the Clustered Index Insert) could possibly result in a duplicate key in the index. Remember there is only one row, one column, and one index.
Logically, the only way this error can occur is if the Delete operator does not delete the row.
Read the whole thing. It’s probably not something you’ll ever come across yourself, hopefully.