Every product marketing org is different, but there are typically three big areas that may or may not be included in a product marketing org including, inbound (working more closely with Product), outbound (or GTM, working more closely with Sales), and compete (often supports competitive needs of Sales or Marketing). On top of that, Product Marketers can often be called upon to support many other functions across Marketing such as demand generation or acquisitions.
If you want to run a Product Marketing team someday, you definitely need some form of experience in all three areas of Product Marketing. I also recommend getting broader marketing experience if possible (e.g., demand gen, acquisitions). If you have a broad set of skills and experiences to draw upon, you will be better equipped to be an effective Product Marketing leader.