Most Software Engineers will follow the same path from Grad to Mid Level to Senior Software Engineer. At this point there are broadly two paths. Some will go down the ‘Team Lead’ path. This would still often be hands on with code but your focus will shift towards people management and leadership.
From there, it's feasible to move into a Software Engineering Manager role and then onto Director, VP or ‘Head of’ Engineering role. From there you would aim to become a CTO. The other path is to move into a ‘Technical Lead’ role. Here you would be still very technically hands-on and you would lead others purely from a technical standpoint to define tasks and make technical decisions.
As your career path evolves, you could then move into a Principle Engineer or Architect role. These are often sole contributor roles.