You Do Need power plug adapter while traveling from Palau 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 Palau are A and B. This is how they look like.

Palau

In Palau, 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