How does the Groovy in operator work?

in is the "Membership operator".

From the documentation for Groovy 3 (emphasis mine):

8.6. Membership operator

The membership operator (in) is equivalent to calling the isCase method. In the context of a List, it is equivalent to calling contains, like in the following example:

def list = ['Grace','Rob','Emmy']
assert ('Emmy' in list)           # (1)    

(1) equivalent to calling list.contains('Emmy') or list.isCase('Emmy')

So, Groovy always calls isCase, which in case of a List maps to contains.

I did some experimentation and it looks like the in operator is based on the isCase method only as demonstrated by the following code

class MyList extends ArrayList {
    boolean isCase(Object val) {
        return val == 66
    }
}

def myList = new MyList()
myList << 55
55 in myList // Returns false but myList.contains(55) returns true     
66 in myList // Returns true but myList.contains(66) returns false

For the JDK collection classes I guess it just seems like the in operator is based on contains() because isCase() calls contains() for those classes.

It's actually all based on isCase. Groovy adds an isCase method to Collections that is based on the contains method. Any class with isCase can be used with in.