Inserting in the middle of the list is still O(1). It doesn't make sense to include finding the insertion position in the insert cost as there are many ways to

Inserting in the middle of the list is still O(1). It doesn't make sense to include finding the insertion position in the insert cost as there are many ways to do that (for example you might have a separate hashed or ordered index, or simply have a pointer to the node by other means). Also, pedantically O(n/2) is the same as O(n).