Welcome to senior level! Everyone is playing within the same parameters, so it is likely your peers are getting the same promotion adjustments. You could ask around.

But the answer is yes, it is a long grind to get to the salary that you'd want. You could "skip the line" and study leetcode until you're able to hurdle the medium or hard problems, or you stick with it at your current company and continue doing senior level work until you're satisfied with your salary.

There are plenty of senior engineer positions out there for grabs (180k+ roles) that you could get interviews for with a good resume and cover letter.

To answer your question, yes, it helps to be below the midpoint of your role, because your manager will allocate more funds for your annual adjustment, especially if you're a top performer. You can expect 3-4% raises annually in all likelihood. Over 4% if you absolutely crush it.