Laid off on EAD from EB1A, can I start an UNRELATED teaching business? Can I travel on Advance Parole?

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I have an EAD from an approved EB1A petition (priority date: Apr 2022). I recently got laid off and am thinking of starting a business ( related to K-12 education.) MY EAD is based on an advanced degree in Operations research with publications and related work experience in data science. Is there a risk to justify 'teaching' or running a tutoring business based on this EAD? If so, can you keep looking for related jobs and teach on the side without incorporating this as a business in the interim? On an unrelated note, in your opinion, what is the risk of traveling out of the country in this situation? (I have an advance parole in hand as well.)
 

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If you have an EB-1A-based EAD and a pending I-485, starting an unrelated business (such as teaching) is risky. Your EB-1A petition asserts that you intend to work in your field of extraordinary ability. Shifting to an unrelated field could raise questions about your original intent and impact your green card application.

Additionally, traveling on Advance Parole in this situation may pose some risks. It’s advisable to either have a job offer or a clear plan to work in your field (such as consulting with clients) before traveling. Proceed with caution.