What is the career path of a front-end developer?

Please do not limit yourself. It is the very best advice I can give you.

The differences between front and back end programming are sometimes discussed as two completely independent areas, although they are not.

Your career is in your hands, no matter what you develop. You do not have to limit yourself to one field if you come from graphics, machine learning, or cryptography, all sub-fields of the software engineer role.

work well as a manager or a senior developer

You will need a thorough understanding of the development process from beginning to end, an open mind, and a desire to learn new things daily.

If you limit yourself to being a front-end developer, no more and no less, you have already closed the door.

Do yourself a favor and think big. Decide what you want to do and go after it; do not try to determine your career solely based on your current experience; you can continually improve and expand your knowledge in other fields if you believe it will help you get closer to the career you want, and do not be fearful to change course if you find yourself regretting previous decisions.

Developers interested in front-end will, in my opinion, be drawn to senior positions and product-related positions such as product management, design, and architecture. However, do not let this limit your options; you could be a CTO, VP R&D, or manage a small team of super developers (ninjas), who knows!