The traditional German PhD is either self-funded or funded through a fixed-term (usually three years) part-time (mostly in the humanities) or full-time (less frequent, mostly in STEM) position at the university at which the PhD is pursued.
Regardless whether full-time or part-time position, you can formally use a certain share of your contractual working time to work on your PhD project. (I don't remember exactly, but probably something like 50 percent.) The remaining part is reserved for unrelated tasks, such as teaching, administration, or other research. This is usually specified in more or less detail in your work contract. In practice, however, your contractual work duties may be more or less related to your PhD project, and if you are lucky, they may even be perfectly aligned or identical. If you have a part-time position, it is generally expected that you also make progress on your PhD thesis during your free time, so that you may complete the thesis within the duration of the fixed-term contract.
It follows that in both traditional and structured PhD programs, and with both full and part-time positions, pursuing a PhD is in general regarded as requiring your full commitment, as if in a full-time job. However, this does not preclude exceptions, which will have to be negotiated on a per-case basis with your institutions and your supervisor.
My guess is that the traditional program offers more flexibility in this regard, because you don't have to follow a certain curriculum, your progress does not have to be aligned with the rest of your cohort, and you don't normally have to complete any coursework.