What are notable certifications/courses that could help in advancing a career in PMM?

I'm glad to hear that you are thinking about certifications -- it's a great way to learn about different product marketing capabilities and get third-party endorsement of your experience. I've never participated in a certification program, but I hear that the Product Marketing Alliance offers a great curriculum in multiple product marketing areas. Check them out (and let me know what you think!).

I really believe doing is the best way to advance your PMM career over certifications. That said, courses can give you a good baseline for frameworks and vocabulary, especially if you are changing careers or just getting started. I've taken these course and have found them useful for getting alignment in a newly formed product marketing team, for example.

However, I really believe there's nothing more powerful than simply time in seat paired with a great network or mentor. My advice instead of taking a course would be to take on a project or program that is uncomfortable or feels out of your wheelhouse to really push yourself to grow. This also show initiative and a curiosity to learn.

I've found Product Marketing Alliance courses to be very helpful. Otherwise, advancing in PMM is really more about on the job experiences than courses/certification. Courses can help you build foundational skills, but advancing into leadership positions is more about demonstrating Strategic Thinking / Vision and Communicating across levels of tenure / detail. For more on those competencies, read my answer to the question about advancing from IC to management.