(log): rename `BaseHandler` to `Handler`

[timreichen]

Is your feature request related to a problem? Please describe.

The name prefix Base is used as an indicator to not create instances of the class but use it as a parent class. It is still possible to create instances though.

Describe the solution you'd like

We should rename the class to Handler and turn it into an abstract class.

Describe alternatives you've considered

Leave as is.