at least draw the extends into the right direction
Are you suggesting that a Login is an extension of Register? The extend relationship is intended to specify "how and when the behavior defined in the extending UseCase can be inserted into the behavior defined in the extended UseCase". If a registration requires a login to be performed as part of it, then that extends relationship is appropriate.
if possible in any way - do not use Login as use case. It is none.
UML describes a use case as: "A UseCase specifies a set of actions performed by its subjects, which yields an observable result that is of value for one or more Actors or other stakeholders of each subject."
Generally the argument against Login as a usecase is the point about value. It certainly meets all of the other criteria of that description. In this era of pervasive tracking a login event has definite value to stakeholders.
While we're at it, a "customer" is a Role, not an Actor. It is an a role being played by an actor
That's exactly what UML says: "An Actor specifies a role played by a user or any other system that interacts with the subject."
So creating an actor for customer is the way the creators of UML intended it to be used.
But Roles can't do anything -they have no agency.
All that means is that the agency playing the role is outside of the scope of UML. It's the role that's the interesting thing, which is why an actor should be named according to the role being played.
It might be worth looking at
the discussion on entity or role for BPMN. Unlike UML, BPMN does provide classes for both.
I have seen a lively discussion about that on LinkedIn where someone argued OMG should have used role rather than actor.
The description of an actor in UML 2.5 reflects that it's about a role being used. Role may be a better pedantic choice of terminology, but actor is a simpler concept (especially for non-technical stakeholders) and fits with the highly iconic stick figure notation.