PhD programme without teaching I know other PhD students (at a different university) who have minimal duties like preparing exercise sheets.

I am going to enter a PhD programme which does not involve any teaching components,
but throughout the years before, I have frequently worked as a tutor, leading exercise classes.

I wonder whether the lack of teaching in my PhD will negatively affect my future employment chances in academia (or whether my teaching experience until now will positively affect my chances). What do you know?
Definitely yes: if in the future you're looking for a teaching (or part-time teaching) position, having less experience than other candidates will be a really bad experience.

Yes to some extent: even for non-teaching research-only positions, teaching experience can be seen as a positive for the applicant. Some of the qualities required for teaching are necessary for other aspects of the job (handling a team, tutoring interns or PhD students, communication with non-scientists, etc.).

So, I would advise you to continue having some teaching duties during your PhD, even if you have to take those outside of your own institution or do some of it pro bono (or for not-so-great pay).