Is the 'existential' a value or ref type?

Using Swift
13

There is hidden achievement to unlock in this setup.

First, we know that the "existential" type itself is a value type which has no value semantics unless it wraps another type with value semantics.

struct Existential<Value> {
  // invisible to the user
  var _value: Value
  // forwards all members of Value
}

Now let's see our protocols:

protocol P0 {
  // this is a `mutating set`
  var x: Int { get set }
}

// protocol is class bound but it still has a `mutating set`
protocol P1: AnyObject, P0 {}

// protocol is class bound but now we re-defined the property
// which implies that the `set` becomes `nonmutating`, it's just
// implicit in this context
protocol P2: AnyObject, P0 {
  var x: Int { get set }
}

// Non-class bound protocol with explicit `nonmutating set`
protocol P3: P0 {
  var x: Int { get nonmutating set }
}

// class bound and implicit `nonmutating set` like P2
protocol P4: AnyObject {
  var x: Int { get set }
}

Now think about how the following values would behave:

Existential<P0>.x = 1 // expected-error
Existential<P1>.x = 1 // expected-error
Existential<P2>.x = 1 // okay
Existential<P3>.x = 1 // okay 
Existential<P4>.x = 1 // okay - this is your first example

// your second example
Existential<P0 & AnyObject>.x = 1 // expected-error
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