No, Zenjob does not provide health insurance.
With Zenjob, you are employed on a short-term basis.
With short-term employment, you are exempt from paying social security contributions. This means that you are not covered by health insurance through Zenjob and must take care of this yourself.
As a student, you are either still covered by family insurance or registered with a student insurance company.
If you use Zenjob as a part-time job and therefore have a main employer subject to social insurance contributions, these contributions are covered by your main employment.