Before I reply, a caution: Given your experience, you are getting into that dangerous area where you might be expensive as an individual contributor. You also may have a tough time keeping up with tech. I strongly recommend continuing to build on tech skills. From test automation, there are a lot of options such as DevOps, CI/CD, API testing, security, performance. You can do these along with your current role. You can also build skills in domains, e.g., salesforce.
There is no easy answer to your question. This also depends on location and industry. In places like India, there are very large teams, and you need managers. In the US and similar, teams aren’t that large and you may not need managers. In large consulting companies, you may need managers.
Don’t focus on learning. You can look for lead/manager roles in your current org. If you are willing to take the risk, you can look for a lead/manager role in a smaller organization.
Explore talking to your manager and others in your organization. It’s difficult to do this online.
It might be good to start by leading projects, i.e., more in a tech role, supervising the work done by a few others. You can see how this goes and then decide the next step. In my experience, when people want to move to a manager role, they are given such responsibilities and then the organization decides what makes sense.
The best resource for learning about management in testing is https://www.amazon.com/Lessons-Learned-Software-Testing-Context-Driven/dp/0471081124 The kindle version is quite affordable.
- Be careful, build tech skills
- Read lessons learned in a few days
- Talk to your manager
- Ask for leading small projects
- Have a backup plan
- Keep reading Lessons Learned
Feel free to ask more questions.