It could be that your current job or organization isn't growing so they won't need more managers.
If that's the case, you need to work for a company that is growing, therefore, opening positions for management. You've mentioned you aren't even motivated to the interview process, so I can tell you for sure you aren't cut for it, at the moment. If it is your hearts utmost desire to become a manager, first you need to work on those thoughts.
Management is a completely different job from a software engineer. It definitely helps to have a lot of engineering knowledge for the context, but your day-to-day activities will be absolutely different from an IC. The emotional state that you've shared on your post really reminds me of an IC, that can likely perform their daily tasks, but won't be able to hold a team together, being lighthearted and caring, also talking about tough subjects with self-awareness.
I'd advise you getting a psychologist and go over and try to figure out why you haven't become a manager yet, and why do you believe you need it, then start working on becoming one.
I for instance, became a manager again after going through therapy and recovering from a big emotional problem (my mother was everything to me, and passed away, and I was a continent far away), it took years and only after that I could see myself having the mental space to deal with other people's problems and desires, which is the main activity you do as a manager.
Also read many books, participated in conferences, made connections, got inspired and so on. That eventually led me to lead a team.
I really doubt the old me could deal with the daily challenges I deal everyday, people dissatisfied, back-to-back meetings etc. I first had to clear up my mind, study to finally arrive in a situation where I could manage others.
Also, by working in tech you've probably also felt how different it is to be led by different people. Some people are ABSOLUTELLY GOOD, others are a pain to work with.
First start writing down and working on those qualities that makes up a good manager to work with. Copy them. Tell them you want to become like them, reach out to them if you no longer work in the same company and tell how they were so good and how you can learn with them.
People are typically very friendly on those requests, and if they see have inspired you in a way, they will be gladly help you and that will help you grow.
Also don't forget you don't need to do this overnight. There are people coding at 60 that are awesome.
FAANG companies also pay much more for senior developers than most directors make in smaller companies. You actually don't need to become a manager to make more money or have more recognition, if that's what you are looking for.
And to be honest, it is very likely that you are enough being just yourself, Today. Don't feel pressured about it. Managers aren't superior in any way, it is just a job, a task that is performed, just like goats climb mountains and birds fly.
Wish you success in your journey!