My two suggestions are: learn everything you can about being a good manager and leader where you are now. Use the time you have as a "new (manager|lead)" in a company that knows you're a "new (manager|lead)" to be the eager newbie (just like you probably did when you were a newbie dev). Find the managers and leaders who you think are good and who have traits that you aspire to have and learn them while you can. Being a good technical manager and leader takes some of the skills of being a good dev, but a whole other set of skills that you generally don't need when being a dev. Finding a good mentor (even if they don't know they're mentoring you) is something you can more easily do at your current company.

When you do look for another job, be up front with the company you're talking to. You may want to interview for a Senior dev position, but tell the recruiter that you want to parlay your experience into being a manager or lead. At my last company, we hired a couple of folks like this, and they almost all turned out to be good managers and leaders.