I have 20 years of experience and right now I am working in a FANG company as a Senior Software Engineer for the past two years. Most of my career I focused on technical skills and whenever I changed jobs I always looked for more challenging technical projects. However, I find that in big companies even engineers with half my experience has the same title as I have even though their technical depth is not very high. These engineers have spent almost all or most their careers in the same company. I realized that most Senior Engineers are focused on solving business problems and stopped going in depth into technology. All of my peers who started out as Software Developers have moved into the managerial path. Having said that I do feel bad of having the same title as someone half my experience and wondering if there is some path where I can continue focusing on technology without just being a person who works on business problems or a manager.
Whether or not it is an option to remain a technical expert at your current job is not really something I, nor anyone else here can likely answer, but it is definitely a career path that exists within certain industries and typically involves some niche specialization. The fact of the matter is that most software being developed today is not terribly technically complex so being skilled at understanding the business domain and being able to advise stakeholders on the best solution is often more important than deep technical skills.
As for your other concern about your title, well that may just be your vanity talking. Titles describe your responsibilities within the company, they aren't a skill ranking. If you do not have signifigantly different responsibilities in your daily work than your fellow Senior Engineers then you don't need a different title. Your compensation is where you should be rewarded for your skill and experience, not your nametag.
I think nowadays is possible to make "a career" working only on technical problems. Of course it depends on your definition of making a career.
You should work on what you want to work, not on what your friends are working. You should work on what you wish to work, not being related on whether people doing the same thing have half or double of your experience. That should not be a factor.
The real reason why developers move to more management roles are two. First, they want to earn more money, and the companies need a reason to justify why they pay team managers more money than the people doing the technical work. By changing the title and the task to a "more management" role, the company has a reason to pay more.
The other reason why many developers change to mild management roles is because they want to show to the world that "they have a promotion".
Nowadays there are developers 50+ totally happy and competent and I also see some managers in their 20s, who although we could argue a bit unexperienced, they proved to be competent already at young ages.
Bottom line: Do the work you want to do, and do not stare at the others. If you feel like continuing doing technical jobs and mild management roles do not appear to you, skip them! Things could change in the future thought. Then reconsider at that time.
This a rather vague question, and can hardly help but be when you ask a bunch of strangers who don't work at your company. We may tell you our eopxeriecne, but they may not apply at your company.
Have you discussed this with your manager? For instance at a regular performance review, when they tend to ask how you see your career developing?
Because that seems to me to be the obvious thing to do.