After your study visa ends, you can stay in Germany by applying for a residence permit for job seekers or employment. The 18-month post-study residence permit allows graduates to seek work related to their field. Once you secure a job, you can switch to a work visa or EU Blue Card if you meet salary and qualification requirements.
Alternatively, you may apply for a freelance visa or further education. Ensure you apply before your current visa expires. Compliance with legal requirements is crucial to avoid penalties. Consult the local immigration office (Ausländerbehörde) for specific guidance based on your situation.