Extending my residence to seek work

I'm reaching out to seek advice regarding my residence in Hamburg. 

I have been living and working in Hamburg since October 18th 2022, originally here on a residence permit for employment (Berufserfahrene,19c). After having my previous bachelor degree finally recognised in Germany this was amended to a blue card (18g) on 2nd December 2024. In may of this year I was unfortunately made redundant, with my last working day the 31st of August, 2025. 

I have notified the Hamburg Welcome Centre of my redundancy and have been searching for a new role since. I am aware that I have 3 months to look for a new role, which takes me to the 30th November, 2025. 

(I have also passed my German B2 Prüfung with Goethe Institut at the beginning of this year, and from July to September of this year I undertook a Weiterbildung in Marketing to increase my job prospects and confidence with terminology relevant to my field in german.) 

As time runs out, I'm looking for advice on my options to extend this 3 month period, either to find another role in line with the blue card criteria or a 'normal' work visa (Zum Arbeiten für Fachkräfte,18a/b) if I can't secure a job that meets the salary threshold for a Blue Card. So far signs seem to point towards applying for a Chancekarte, which would allow to me stay beyond the end of November and continue to look for a new job.

Any advice on case would be so very welcome, I would really like to stay here and apply for a Niederlassungserlaubnis in the future. (that was my plan for next year once I had completed 21 months on the Blue Card.)