You Do Need power plug adapter while traveling from Taiwan to Vatican City.

Here is Why You Need An Adapter

The outlet and plug type used in Vatican City are C, F and L and in Taiwan are A and B. This is how they look like.

Taiwan

In Taiwan, outlets of type A and B are in use.

Type A

Type B

Vatican City

In Vatican City, outlets of type C, F and L are in use.

Type C

Type F

Type L