Semantics of Member Provided via Protocol Conformance

If a type obtains a method or computed property by conforming to a protocol, is that method or property a member of the type? I'm not sure of the semantic intent behind the concept.

For example:

protocol P { var id: String { get } }
extension P { var id: String { "P" } } 

class C: P {}

class D: C {
  override var id: String { "D" } // ERROR - if override keyword  is removed, no error

By conforming to P, C gains the ability to access an id property and a default implementation for it.

I understand that, when I access id directly on C, that access does not go through the protocol conformance (i.e., it does not check the witness for the id requirement). Instead, it statically dispatches directly to id. Semantically, that feels like id is a member of C.

OTOH, when I declare D as a subclass of C, and then override the id property of C, I trigger an error: "Property does not override any property from its superclass." The compiler is telling me that C does not have a property named id. If I remove the override keyword, the code compiles, and the usual error that one would get when overriding without using the override keyword is not generated ("Overriding declaration requires an 'override' keyword"). Semantically, that feels like id is NOT a member of C.

So, which is it? Is id a member of C or not?

If id is not a member of C, then what are the semantics of accessing id on C?

In this regard, consider the following statement made in the Language Reference refrained the nature of an extension declaration:

If the type name [of an extension] is a protocol type, the extension extends all types that conform to that protocol.

Thus, the extension on P should be regarded as extending C, thus including the id declaration as a member of C.