Just a slightly different angle. The best managers and team builders are people that aren't afraid to get people in with skills far out pacing their own. Maybe some one can program this task better than you but the company has trust in you to find those people and put them in the best environment to leaverage that skill. The best skill you can have is using other people's skills together. No body wants a manager who can only program. They want a leader and some one who is knowledgeable in their peticular code base. A programming test shows they can program but doesn't mean they'll have the years of knowledge of your code base that you do

I see it as a different skillset. You possess skills to cut maintainable code, work through issues (technical and people), and whatever other traits the organisation sees you doing well in, or have the potential to. That is quite different from interviewing, which is often just about impressing people enough to let you in the door. I say this having gone through the same process. If you're that worried, study the code as you're already doing, grind leetcode, or my preference - pick up harder problems and run with them. You'll learn some new stuff, maybe build something cool and feel a bit less like an imposter.