Am I eligible for EAD auto extension under eligibility category C09 if my previous eligibility category was C3C?

Automatic extensions for EADs involve the same class of EAD and not different classes. That is because USCIS has already seen the basis for and approved the initial EAD application and is not so concerned about issues of ineligibility when considering an extension. In your case, it saw and considered your STEM extension application previously and so allowed your automatic work extension during the pendency. It will not give the same treatment for your initial EAD based upon adjustment of status, an entirely different basis for benefit. Due to the limitations of the Lawyers.com Forums, Alan Lee & Arthur Lee, Esqs.’ (the "Firm") participation in responding to questions posted herein does not constitute legal advice, nor legal representation of the person or entity posting a question. No Attorney/Client relationship is or shall be construed to be created hereby. The information provided herein by the Firm is general, and requires that the poster obtain specific legal advice from an attorney. The poster shall not rely upon the information provided herein as legal advice nor as the basis for making any decisions of legal consequence.