What degree do I need to pursue a role related to Product Management/Strategy?

21(M) here. I’ve currently gotten an offer as either an Associate Program Manager or an Associate Product Manager at a startup (I’ll get to know by the end of this month). I plan on pursuing my education further by getting an MBA but I’m unsure regarding which domain would best suit my career growth. I also wanted to know if it’s absolutely necessary to go through roles that require you to code (such as an SDE) in order to get to a higher position in product. Any suggestions?

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