Management not being a promotion doesn’t mean that managers aren’t (usually—I’ve both been at equal and higher levels than my managers at times) higher levels than their reports. It means that switching to a management role from IC is never a promotion itself (ie always L6 -> M1 in Google/Meta levels) and it never comes with any difference in compensation.
I haven't been a manager, but my understanding is that the higher IC roles assume you're competent enough to do some management-like things if needed ("responsibility without control"), and I also assume that being a manager helps with compensation because they actually teach you how the review process works and let you into the calibration meetings.
