Transparency regarding the processing of personal data in online services is a necessary precondition for informed decisions on whether or not to share personal data. In this paper, we argue that privacy interfaces shall incorporate the context of display, personal preferences, and individual competences of data subjects following the principles of universal design and usable privacy. Doing so requires -- among others -- to consciously decouple the provision of transparency information from their ultimate presentation. To this end, we provide a general model of how transparency information can be provided from a data controller to data subjects, effectively leveraging machine-readable transparency information and facilitating versatile presentation interfaces. We contribute two actual implementations of said model: 1) a GDPR-aligned privacy dashboard and 2) a chatbot and virtual voice assistant enabled by conversational AI. We evaluate our model and implementations with a user study and find that these approaches provide effective and time-efficient transparency. Consequently, we illustrate how transparency can be enhanced using machine-readable transparency information and how data controllers can meet respective regulatory obligations.